# How do you solve 7^(x – 2) = 12x?

Nov 1, 2015

A step in the correct direction!! Perhaps someone else can take it further. I used the Iteration method.

#### Explanation:

$\textcolor{red}{\text{Method 1}}$
Plot the straight line graph of $12 x$
Plot the curve of ${7}^{x - 2}$
The intersections are where the values for $x$ are.

Or try iteration for $x = {7}^{x} / 588$

$\textcolor{red}{\text{Method 2}}$
${7}^{x - 2} \to \frac{{7}^{x}}{{7}^{2}}$

so ${7}^{x - 2} = 12 x \to {7}^{x} = \left({7}^{2}\right) \left(12\right) x$

${7}^{x} = 588 x$

Taking logs
$x \ln \left(7\right) = \ln \left(588\right) + \ln \left(x\right)$

$x = \frac{\ln \left(588\right) + \ln \left(x\right)}{\ln \left(7\right)}$

By iteration

Set seed value as 1
$x \cong 3.988$ to 3 decimal places

I could not find the seed for the lower one which is in the region of
$x \cong 0.0016$ to 5 dp

Graphs of the log method: