Use following log property:
[tex]ln( a^n) = n ln (a)[/tex]
Take log of both sides
[tex]ln (10^{2x+9}) = ln (290) \\ \\ (2x+9) ln (10) = ln (290)[/tex]
Distribute left side, isolate 'x'
[tex]2 ln (10) x + 9 ln(10) = ln (290) \\ \\ x = \frac{ln (290) - 9 ln(10)}{2 ln(10)}[/tex]
