Learn how to solve any exponential equation of the form a⋅b^(cx)=d. For example, solve 6⋅10^(2x)=48.
Log in Cookenmaster, Cheyenne 8 years agoPosted 8 years ago. Direct link to Cookenmaster, Cheyenne's post “In number 5, where did th...” In number 5, where did the 1/2 come from. Why... Actually, it would be great if the whole problem is explained to me, but differently. It doesn't make sense to me. • (18 votes) InnocentRealist 8 years agoPosted 8 years ago. Direct link to InnocentRealist's post “I didn't use "1/2" and I ...” I didn't use "1/2" and I don't think it's really necessary: 1) 4*(5^(2*x)) = 300 2) 5^(2*x) = 75 (At this point you can just take the log of both sides (see below) and that's where the 1/2 comes from), or: 3) (5^2)^x = 75 (laws of exponents) 4) 25^x = 75 5) x = log_25(75) (log form) 6) x = log75/log25 = 1.341 (change of base rule) Or for 3) you could do: 3) log_5(5^(2*x)) = log_5(75) (log form) 4) 2*x = log_5(75) (Here's where 1/2 comes in) 5) x = (1/2)log_5(75) 6) x = (1/2)(log75/log5) = 1.341 (26 votes) aditya 7 years agoPosted 7 years ago. Direct link to aditya's post “while practicing a questi...” while practicing a question came to my mind. It maybe stupid,but I am going to ask it anyway. we have a subtraction property(log a-log b=log a/b) and change of base property(log_a b=log b/log a). I can understand when it goes in the said direction.but when it is applied in reverse how do i differentiate eg. log a/log b how so i determine which property to apply. • (8 votes) Katriana 4 years agoPosted 4 years ago. Direct link to Katriana's post “Your question was a long ...” Your question was a long time ago, but here is an answer for anyone that may be wondering. Ruzbah Aria 6 years agoPosted 6 years ago. Direct link to Ruzbah Aria's post “Can anybody help:log_5 y...” Can anybody help: • (7 votes) bhvima 6 years agoPosted 6 years ago. Direct link to bhvima's post “Really nice question! You...” Really nice question! You need to know the properties of logarithms in order to solve this problem. The answer is y = x=5^(3-2√2) Hope this helps. (10 votes) Claire Z a year agoPosted a year ago. Direct link to Claire Z's post “cant wait to come back ye...” cant wait to come back years from now and realize i still cant do algebra 2 • (11 votes) b.k.phillips 7 years agoPosted 7 years ago. Direct link to b.k.phillips's post “Can someone walk me throu...” Can someone walk me through the last challenge question? I see solving for each zero as they suggested, but am curious if one can expand it out as a quadratic to solve. When I try to do this, I keep coming out w incorrect solutions. CHALLENGE QUESTION: Which of the following are solutions to (2^x-3)(2^x-4)=0 My approach is giving me {WHEN SETTING 2^x =y}: which then gives me a quadratic formula of; which results in values of 4 and 3. I assume I am making an error, perhaps in setting the y or somewhere else regarding my treatment in expanding the equation, but I am not finding it; any help is appreciated. • (4 votes) Duymayan, Beyza 7 years agoPosted 7 years ago. Direct link to Duymayan, Beyza's post “In this setting we are so...” In this setting we are solving for x, and how nice of them, to already give it to us factored out. When this quadratics is factored out this way, it means we are 1 step away from finding x itself. Both set of equations equal to 0 since we separated the into two individual parts. 2^x - 3 = 0 This is how it is sorted out. If you still have questions, please comment :) (7 votes) DaySatyr5771669 10 months agoPosted 10 months ago. Direct link to DaySatyr5771669's post “Hi I was wondering if you...” Hi I was wondering if you could help me with this question? • (4 votes) Edward Miotke 9 months agoPosted 9 months ago. Direct link to Edward Miotke's post “I believe that the short ...” I believe that the short answer is: x = 2a. Below is an explanation of how I got to that answer: Start with: 3log_a (x) = 3 + log_a (8) Since 1 = log_a (a), we can rewrite the equation as: Finally, after canceling the log from both sides we get: x = 2a. I hope that this is helpful. (5 votes) ys1006679 a year agoPosted a year ago. Direct link to ys1006679's post “log down 4 (2x/x-1)=2” log down 4 (2x/x-1)=2 • (2 votes) Kim Seidel a year agoPosted a year ago. Direct link to Kim Seidel's post “Switch the equation into ...” Switch the equation into exponential form to solve: Hope this helps. (6 votes) Amy Shaffer a year agoPosted a year ago. Direct link to Amy Shaffer's post “Zero product rule does no...” Zero product rule does not yield same result as quadratic rule from unit 2 lesson 6. Quadratic yielded (17+- 1)/12 = 1.5 or 1.3333. Explain. • (1 vote) Kim Seidel a year agoPosted a year ago. Direct link to Kim Seidel's post “This questions doesn't ap...” This questions doesn't apply to to this lesson. Please post your question in the lesson you are asking about. Without knowing the actual original problem and the answers derived for that problem, it is impossible to give you an answer. (7 votes) george johnston 7 years agoPosted 7 years ago. Direct link to george johnston's post “What exactly is going on ...” What exactly is going on when you have to change the base rule? I don't really follow that part of these equations • (3 votes) Thessalonika 7 years agoPosted 7 years ago. Direct link to Thessalonika's post “Did you watch the last se...” Did you watch the last section of videos "The Change of Base Formula for Logarithms"? That really helped me, since I'd never heard of changing bases before. Here's a link to the first video: (3 votes) trevor pummell 8 years agoPosted 8 years ago. Direct link to trevor pummell's post “How do you do the followi...” How do you do the following problem log4n=1.5log416+1.3log464 • (2 votes) R_H_ 6 months agoPosted 6 months ago. Direct link to R_H_'s post “Assuming this is the prob...” Assuming this is the problem: log_4(n) = 1.5log_4(16) + 1.3log_4(64) 1) log_4(16) = 2 and log_4(64) = 3 So we have : log_4(n) = 1.5(2) + 1.3(3) 2) log_4(n) = 6.9 This is equivalent to: 4^(6.9) = n 3) 14,263.1 ≈ n (1 vote)Want to join the conversation?
The subtraction property says that log(a)-log(b) is equal to log(a/b).
The change of base property says that log_a(b) is equal to (log_x(b))/(log_x(a)).
So, in the subtraction property the division is within the log, while for the change of base property we are really dividing the answers from the two logs.
So, if we are given log(a/b) to expand, we can use the subtraction property; if we are to condense (log(b))/(log(a)), then we should use the change of base property.
I had a little difficulty understanding how to tell the difference myself at first. Hopefully this explanation was written clearly enough.
log_5 y+log_y 5= 6 ?
It would be too tedious to type out the answer for you, so instead I linked it in this graph step by step.
https://www.desmos.com/calculator/9teeitvqjp
y^2-7y+12=0
7+or- sqrt(49-4(12)) all over 2
2^x = 3
x = log base 2 parentheses 3 is one of the answers.2^x - 4 = 0
2^x = 4
2 * 2 = 4
x = 2 as the other answer.
"Find the value of x in terms of a, where 3 log(base a)x=3+log(base a) 8"
Thanks
Multiply both sides by 1/3: log_a (x) = 1 + (1/3)log_a (8)
After using the power rule we get: log_a (x) = 1 + log_a (8^(1/3))
which simplifies to: log_a (x) = 1 + log_a (2)
log_a (x) = log_a (a) + log_a (2)
Next, using the Product Rule we get: log_a (x) = log_a (2a)
2x/x-1 = 4^2
Simplify the exponent: 2x/x-1 = 16
Then, assuming your expression inside the parentheses is (2x)/(x-1), you can cross multiply to get: 2x=16(x-1), and solve for "x".
https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/change-of-base-formula-for-logarithms/v/change-of-base-formula
