Consider the following 54x 1 6 a Find the exact solution of

Consider the following.

5^(4x 1) = 6

(a) Find the exact solution of the exponential equation in terms of logarithms.

(b) Use a calculator to find an approximation to the solution rounded to six decimal places.

Solution:

Given the Equation

5^{(4x 1)} = 6

Assume That

5^{(4x 1)} = 6

Apply Log on both sides

log(5^{(4x 1)}) = log 6

(4x-1) log 5 = log 6

4x-1 = log 6/(log 5)

4x = log 6/(log 5) - 1

4x = 0.1132827

x = 0.0283207