How do you solve 10^(4x-1) = 5000? Precalculus Solving Exponential and Logarithmic Equations Logarithmic Models 1 Answer VNVDVI 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 Answer link Related questions What is a logarithmic model? How do I use a logarithmic model to solve applications? What is the advantage of a logarithmic model? How does the Richter scale measure magnitude? What is the range of the Richter scale? How do you solve 9^(x-4)=81? How do you solve logx+log(x+15)=2? How do you solve the equation 2 log4(x + 7)-log4(16) = 2? How do you solve 2 log x^4 = 16? How do you solve 2+log_3(2x+5)-log_3x=4? See all questions in Logarithmic Models Impact of this question 1577 views around the world You can reuse this answer Creative Commons License