How do solve this exponential equation for the variable?: 36^x= 1/216 My teacher told me to use natural log: ln My teacher also told me to use log base: I guess that is e
We can rewrite 36 as an exponential with base 6.
Take note that 6*6 = 36. So, 36 = 6^2.
We can also rewrite 216 as an exponential with base 6.
Take note that 6*6*6 = 216. So, 216 = 6^3.
So, we will have:
`6^(2x) = 1/6^3`
We can use the property: 1/a^m = a^-m.
`6^(2x) = 6^-3`
Take the natural logarithm of both sides.
`ln6^(2x) = ln6^-3`
Use the property: lna^b = blna.
`(2x)ln6 = -3ln6`
Divide both sides by ln6.
`2x = -3`
Divide both sides by 2.
`x = -3/2`
Therefore, the answer is x = -3/2.