How do you solve $6 \cdot 17^{a} + 4 = 20$ $6*17^a+4=20$ ?

Question

1821 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-22T03:09:00

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

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

${log}_{10} 17^{a} = {log}_{10} 8 - {log}_{10} 3$ $log_10 17^a =log_10 8 - log_10 3$

$a ({log}_{10} 17) = 0.426$ $a(log_10 17) = 0.426$

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

$a = 0.346$ $a = 0.346$

Checking,

$6 \cdot 17^{0.346} + 4$ $6*17^(0.346) + 4$

$6 \cdot 2.67 + 4$ $6*2.67 + 4$

$16.02 + 4$ $16.02 + 4$

$20.02$ $20.02$ which is reasonably close to twenty.

How do you solve 6*17^a+4=206⋅17a+4=206*17^a+4=20?