`4^x = 16` Solve for `x`.

Textbook Question

Chapter 3, 3.4 - Problem 7 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Another method to solve this problem is to use logarithms (either log or ln, I prefer the latter). Use the ln and then use it's properties to solve for x.

Given

`a^x=b `

Then,

`lna^x=lnb `

and then,

`xlna=lnb `

Make sure you do the same thing on both sides!

`ln4^x=ln16 `

`xln4=ln16 `

Divide both sides by `ln4 `

`x=ln16/ln4 `

Simplify,

`x=2 `

Note that you should get the same answer if you used the other method. If you don't then recheck your work because you must have made a mistake along the way!

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