# How do you solve 10 ^( 2x+1 )= 50?

Mar 7, 2016

x = $\frac{\log 5}{2}$

#### Explanation:

log ${a}^{m}$ = m log a.
log ${10}^{2 x + 1}$ = (2x +1) log10 and log 10 =1.
log (ab) = log a + log b.
log 50 = log 5 + log 10 = log 5 + 1.
Logarithms (of any base ) of expressions on both sides are equal
The convenient choice here is common logarithm.
2 x = log 5..