Solve the following exponential equation.

Question

Solve the following exponential equation. Express the solution in set terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.

2^{0.9x = 291}

Answer 1

Hello Be.,

Take natural log of both sides:

ln 2^0.9x = ln 291

0.9x * ln2 = ln 291

Then divide both sides by ln2: 0.9x = ln 291/ln2

Then divide both sides by 0.9: x = ln 291/ (0.9*ln2)

That is the exact solution. You would then plug this in your calculator.

Cheers.