Question

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

Answer 1

x = `( log 5 )/2`

Explanation:

log `a^m` = m log a.
log `10^(2x+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..