You're faced with an equation where the variable 'x' is trapped in the exponent, like 2ˣ = 100. How do you free it?

You cannot use normal algebra. You need a special key to unlock the exponent. That key is the logarithm.

The Strategy: Take the logarithm of both sides of the equation.

You can use any base logarithm you want, but the common log (log₁₀) or the natural log (ln) are usually easiest.

So, 2ˣ = 100 becomes log(2ˣ) = log(100).

Now, use the most powerful law of logarithms: the Power Rule. It allows you to bring the exponent down in front as a multiplier.

The equation magically transforms into: x * log(2) = log(100).

'x' is no longer trapped! It's now a simple multiplication problem.

To solve for x, just divide both sides by log(2).

So, x = log(100) / log(2). You can now plug this into your calculator to get the final answer.