How do you solve 10^(4x-1) = 5000?

1 Answer
Mar 2, 2018

x=ln(5000)/(1ln(4))+1/4

Explanation:

Apply the natural logarithm to both sides:

ln(10^(4x-1))=ln(5000)

ln(10^(4x-1))=(4x-1)ln(10), as the exponent property for logarithms tells us that ln(x^y)=yln(x).

ln(10^(4x-1))=ln(5000)hArr(4x-1)ln(10)=ln(5000)

Solve for x:

((4x-1)cancelln(10))/cancelln(10)=ln(5000)/ln(10)

4xcancel(-1+1)=ln(5000)/ln(10)+1

(cancel(4)x)/cancel4=ln(5000)/(4ln10)+1/4