# How do you solve this exponential equation for the variable?: 3^r-3= 1/3 My teacher told me to use natural log: ln My teacher also told me to use log base: I guess that is e

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Expert Answers

violy | Certified Educator

We can use the property:

`1/a^m = a^-m`

We will have:

`3^(r - 3) = 3^-1`

Take the natural logarithm of both sides.

`ln3^(r - 3) = ln3^-1`

Use the property: `lna^b = blna`

` ``(r - 3)ln3 = -1ln3 `

Divide both sides by ln3.

`r - 3 = -1`

Add 3 on both sides.

`r = 2`

Therefore, **the answer is r = 2**.