SOLUTION: 8^(x+3)=9^x x=52.965 but please explain how to get there.

Question 1000716: 8^(x+3)=9^x
x=52.965 but please explain how to get there.
Found 2 solutions by fractalier, MathLover1:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
From 8^(x+3)=9^x, apply laws of logs to get
log(8^(x+3))=log(9^x)
and
(x+3)log8 = xlog9
xlog8 + 3 log 8 = x log 9
Collect like terms and solve for x...
xlog8-xlog9 = - 3log8
x(log8-log9)=-3log8
x = -3log8 / (log8-log9)
Now plug in values
x = -3(.903)/(.903-.954)
x = 52.965
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

...........since and , we have

or, rounded to three decimals

RELATED QUESTIONS
e^(x)+e^(-x)=3 x=0.9624 and -0.9624 but please explain how to get there.... (answered by fractalier,Alan3354)
logx=6 x is 1,000,000 but please explain how to get there.... (answered by fractalier)
Please explain how to get the answer for: (4x+3)(3x-1)-(5x-3)(x+2)=(7x+9)(x-3) The... (answered by stanbon)
|sqrt(x+3)-((7+x)/4)|<0.5 How to solve this inequality? I get -2.07 (answered by greenestamps)
|sqrt(x+3)-((7+x)/4)|<0.5 How to solve this inequality? I get -2.07>x>1.9 But... (answered by ikleyn)
What is the product of the roots of this equation? 2Xsquared+ 8/9 = 3 1/3 x The... (answered by vleith,checkley77)
10x-(3-x)= 2(x+3)+ 9. The teacher says the answer is x=2, but i must show how to get that (answered by stanbon)
MY SON HAS THIS PROBLEM TO DO AND I CAN NOT FIGURE IT OUT. CAN YOU PLEASE EXPLAIN HOW TO... (answered by wilft1)
Solve the exponential equation: 8^x - 3(8^-x) = 2 My answer key says it's x =... (answered by MathTherapy)