Question

Solve 10 ^(2x+9)=290 Express in terms of natura logarithms

Answer 1

Use following log property:
$ln( a^n) = n ln (a)$

Take log of both sides
$ln (10^{2x+9}) = ln (290) \\ \\ (2x+9) ln (10) = ln (290)$

Distribute left side, isolate 'x'
$2 ln (10) x + 9 ln(10) = ln (290) \\ \\ x = \frac{ln (290) - 9 ln(10)}{2 ln(10)}$