SOLUTION: for each pair of equations, solve one of them by taking logs of both sides. Solve the other by expressing both sides as a power of the same number. A. 9^x = 4 B. 9^x = 3/3^x

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Question 196795: for each pair of equations, solve one of them by taking logs of both sides. Solve the other by expressing both sides as a power of the same number.
A. 9^x = 4
B. 9^x = 3/3^x
Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!



Take logs of both side:



Use a rule of logarithms on the left



Divide both sides by 









-------------------



Write  as 

Write  on the right as 



Multiply inner exponent by outer exponent on
the left side.

Subtract the exponents on the right:



Since the bases on each side are positive and
not equal to 1, we can equate the exponents:









Edwin
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
for each pair of equations, solve one of them by taking logs of both sides. Solve the other by expressing both sides as a power of the same number.
A. 9^x = 4
Taking the log of both sides you get:
x*log(9) = log(4)
x = [log(4)]/[log(9)]
x = 0.6309....
=========================
B. 9^x = 3/3^x
Converting both sides to powers of 3 you get:
3^(2x) = 3^(1-x)
Then 2x = 1-x
3x = 1
x = 1/3
=========================
Cheers,
Stan H.
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