Question

Solve the exponential equation. (logs) 3(1.05)^x+1=6

Answer 1

$\bf 3(1.05)^x+1=6\implies 3(1.05)^x=5\implies (1.05)^x=\cfrac{5}{3}\\\\ -----------------------------\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\qquad thus\\\\ -----------------------------\\\\ log\left[ (1.05)^x \right]=log\left( \cfrac{5}{3} \right)\implies xlog\left[ (1.05) \right]=log\left( \cfrac{5}{3} \right) \\\\\\ x=\cfrac{log\left( \frac{5}{3} \right)}{log(1.05)}$