Solve for x: 27^5x−7=(1/81)^8x−3

Going off memory it appears like a problem that will need natural logs... Therefore, I'd solve it this-a-way:

27^5x−7=(1/81)^8x−3

{Rewritten using one of the natural log rules.}

(5x-7)ln(27)=(8x-3)ln(1/81)

{Im gona go ahead and solve the natural log of 27 and 1/81 - and then distribute. May get messy}

(5x-7)(3.2958)=(8x-3)(-4.3944)

{Distribute.}

16.4791x-23.0709=-35.1556x+13.1833

{And solve.}

16.4791x-23.0709=-35.1556x+13.1833
both sides: +23.0709

16.4791x = -35.1556x+36.2542
both sides: +35.1556x

51.6347x = 36.2542
both sides: (/51.6347)

x = .7021

Due to me rounding most the numbers to 4 decimal places, your answer may differ slightly from mine.