SOLUTION: Solve: 8^(4x-3)= 1/16, find the exact answer.

Question 34528: Solve:
8^(4x-3)= 1/16, find the exact answer.
Found 2 solutions by venugopalramana, josmiceli:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
8^(4x-3)= 1/16,
(2^3)^(4X-3)=1/(2^4)=2^(-4)
2^(12X-9)=2^(-4)
12X-9=-4
12X=-4+9=-5
X=-5/12
find the exact answer.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

note that

multiply both sides by 8^3

take log base 10 of both sides

note that

check this by subbing in the original equation
I get
this is true- checks
------------------
note also-

this is a more "exact" answer, since there is no rounding to a certain number
of decimal points

RELATED QUESTIONS
For the following, solve. Find exact solutions... (answered by jim_thompson5910)
solve for x. 15^(8x)=16^(x+8) Write the exact answer using base-10 logarithms. (answered by josgarithmetic)
find the exact value log3 1/27+ (16) -3/4 and solve the equation log4 (x+5) + log4 (answered by stanbon)
By solving {{{x^4 + 4x^3 -6x^2 -4x +1 = 0 }}} another way, show that the exact value of... (answered by CPhill)
First estimate answer. Then multiply to find the exact answer.Simplify all answers: 8 1/8 (answered by MathLover1)
Find the exact solutions to {{{x^2+4x+4=16}}} (answered by jim_thompson5910)
Solve the logarithm equation. Type exact answer.... (answered by Alan3354)
Solve for X: 9 ^(-x-3) = 14 ^(-4x) Write the exact answer using base-10... (answered by htmentor)
1/8-3/4x=1/16 (answered by bonster)