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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

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

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

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