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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

9%5Ex=4

Take logs of both side:

log%289%5Ex%29=log%284%29

Use a rule of logarithms on the left

x%2Alog%289%29=log%284%29

Divide both sides by log%289%29

%28x%2Alog%289%29%29%2F%28log%289%29%29=%28log%284%29%29%2F%28log%289%29%29



x+=+.6020599913%2F.9542425094

x+=+.6309297536

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

9%5Ex+=+3%2F3%5Ex

Write 9 as 3%5E2

Write 3 on the right as 3%5E1

%283%5E2%29%5Ex+=+3%5E1%2F3%5Ex

Multiply inner exponent by outer exponent on
the left side.

Subtract the exponents on the right:

3%5E%282x%29=3%5E%281-x%29

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

2x=1-x

2x%2Bx=1

3x=1

x=1%2F3

Edwin

Answer by stanbon(75887) About Me  (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.