How do you solve 3(2)^(x-2)+1=100?

Oct 8, 2015

$x = {\log}_{2} \left(33\right) + 2$

Explanation:

As it is written, the answer does not look well rounded.
Here is the solution of the original equation
$3 \cdot {2}^{x - 2} + 1 = 100$

subtract $1$ from both sides:
$3 \cdot {2}^{x - 2} = 99$

divide by 3 both sides:
${2}^{x - 2} = 33$

apply ${\log}_{2} \left(\right)$ to both sides:
$x - 2 = {\log}_{2} \left(33\right)$

add $2$ to both sides:
$x = {\log}_{2} \left(33\right) + 2$