# If the graph of y=AB^x passes through the points (2,3) and (5,81), then what is the value of B?

Feb 27, 2017

$B = 3$

#### Explanation:

Substitute the 2 given points into the equation.

$\left(2 , 3\right) \to 3 = A {B}^{2} \to \left(1\right)$

$\left(5 , 81\right) \to 81 = A {B}^{5} \to \left(2\right)$

$\text{dividing "(2)" by } \left(1\right)$

$\Rightarrow \frac{\cancel{A} {B}^{5}}{\cancel{A} {B}^{2}} = \frac{81}{3}$

$\Rightarrow {B}^{3} = 27$

$\Rightarrow B = 3$