How do you solve 6*14^k+4=76?

Sep 18, 2016

$\textcolor{\mathrm{da} r k red}{k} = 0.9416$

Explanation:

As with a normal equation, isolate the term or factor which contains the variable.

$6 \times \textcolor{\to m a \to}{{14}^{k}} + 4 = 76 \text{ } \leftarrow$ subtract 4 from both sides

$6 \times \textcolor{\to m a \to}{{14}^{k}} = 72 \text{ }$ divide by 6 on both sides

$\textcolor{\to m a \to}{{14}^{k}} = 12$

12 is clearly not an exact power of 14, so logs are indicated.

$\log {14}^{\textcolor{\mathrm{da} r k red}{k}} = \log 12 \text{ } \leftarrow$ apply the log power law

$\textcolor{\mathrm{da} r k red}{k} \log 14 = \log 12 \text{ } \leftarrow$ isolate k

$\textcolor{\mathrm{da} r k red}{k} = \log \frac{12}{\log} 14 \text{ } \leftarrow$ use a calculator

$\textcolor{\mathrm{da} r k red}{k} = 0.9416$