Question

Solve for x using logs-

2*7^x=17*3^x

Answer 1

`2\cdot7^x=17\cdot3^x\ \ \ \ |\log\\\\\log(2\cdot7^x)=\log(17\cdot3^x)\ \ \ \ |use\ \log (x\cdot y)=\log x+\log y\\\\\log2+\log7^x=\log17+\log3^x\ \ \ \ |-\log2;\ |-\log3^x\\\\\log7^x-\log3^x=\log17-\log2\ \ \ \ |use\ \loga^n=n\log a\\\\x\log7-x\log3=\log17-\log2\\\\x(\log7-\log3)=\log17-\log2\ \ \ |use\ \log x-\log y=\log(x)/(y)\\\\x\log(7)/(3)=\log(17)/(2)\ \ \ \ |:\log(7)/(3)\\\\\boxed{x=(\log(17)/(2))/(\log(7)/(3))}`