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 196782: 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

Answer by Edwin McCravy(20063) 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