Consider the following 54x1 4 a Find the exact solution of

Consider the following.

5^4x-1 = 4

(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

5^(4x -1) =4

taking log of both sides:

log{ 5^(4x -1) } = log4

(4x -1)log5 = log4

4x -1 = log4/log5

4x = 1+log4/log5

a) x = ( log5 +log4)/4log5

b) Plugging values log4 and log5 from calculator:

x = 0.465338