# How do you solve 2^(3x)=64 using a graph?

Feb 25, 2017

The solution is $x = 2$

#### Explanation:

To solve the equation ${2}^{3 x} = 64$,

one should draw the graph of $y = {2}^{3 x} - 64$

It is apparent that as $x \to - \infty$, ${2}^{3 x} \to 0$ and $y \to - 64$

Some other values will be when $x = 0$ $y = - 64$; when $x = 1$ $y = - 56$; when $x = \frac{4}{3}$ $y = - 48$ and when $x = \frac{5}{3}$ $y = - 32$

and graph appears as follows:
graph{2^(3x)-64 [-4, 4, -75, 75]}

As the graph intersects $x$-axis at $\left(2 , 0\right)$

the solution is $x = 2$