# How do you solve 6*17^a+4=20?

Mar 22, 2018

$6 \cdot {17}^{a} = 16$

$3 \cdot {17}^{a} = 8$

${\log}_{10} {17}^{a} = {\log}_{10} 8 - {\log}_{10} 3$

$a \left({\log}_{10} 17\right) = 0.426$

$a = \frac{0.426}{1.23}$

$a = 0.346$

Checking,

$6 \cdot {17}^{0.346} + 4$

$6 \cdot 2.67 + 4$

$16.02 + 4$

$20.02$ which is reasonably close to twenty.