How do you solve log_5 x + log_10 x = 4? Precalculus Solving Exponential and Logarithmic Equations Logarithmic Models 1 Answer Shwetank Mauria Mar 25, 2016 x=44.228 Explanation: As log_b x=log_ax/log_ab, we have log_5x+log_10x=4 can be written as log_10x/log_10 5+log_10x=4 or log_10x/0.699+log_10x=4 or log_10x+0.699xxlog_10x=4xx0.699 or log_10x(1+0.699)=4xx0.699 or log_10x=(4xx0.699)/1.699=1.6457 x=10^(1.6457)=44.228 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 1658 views around the world You can reuse this answer Creative Commons License