Question

Solving Exponential Equations with Logarithms Solve each equation. Round your answers to the nearest ten-thousandth.

1) 3^b = 17 2) 12^r= = 13
3) 9^n = 49 4) 16^v = 67
5) 3^a = 69

Answer 1

1. =2.5759 ; 2. =0.8290 ; 3. =2 ; 4. =1.7959 ; 5. = 3.9138

Explanation:

1. Taking logarithm with base 3 on both sides, we get:

b = log₃(17)

b ≈ 2.5759

2. Taking logarithm with base 12 on both sides, we get:

r = log₁₂(13)

r ≈ 0.8290

3. Taking logarithm with base 9 on both sides, we get:

n = log₉(49)

n = 2

4.Taking logarithm with base 16 on both sides, we get:

v = log₁₆(67)

v ≈ 1.7959

5.Taking logarithm with base 3 on both sides, we get:

a = log₃(69)

a ≈ 3.9138