# How do you solve for x in 6 = 15^(1-x)?

May 2, 2016

Use logs to calculate: $x = 0.338$

#### Explanation:

The variable is in the index and 6 is definitely not a power of 15, therefore logs are called for...

Log both sides: $\log 6 = \log {15}^{1 - x}$

Power law: log 6 = (1-x) log 15

isolate (1-x): $\frac{\log 6}{\log 15} = 1 - x$

With a calculator: $1 - x = 0.6616$

$$                             0.338 = x#