Bukit Panjang 2010 P1 Q3a Logarithm Question Solution (A Maths Tuition)

Question:
Solve the following equation:

(a) 5^{2x}-7^x-35(5^{2x})+36(7^x)=0

Solution:

-34(5^{2x})+35(7^x)=0

35(7^x)=34(5^{2x})

Ln both sides, we get

\ln 35 + x\ln 7=\ln 34+2x\ln 5

\ln 35-\ln 34=x(2\ln 5-\ln 7)

\displaystyle \boxed{x=\frac{\ln 35-\ln 34}{2\ln 5-\ln 7}=0.0228}