Question

How do you solve `5(2)^(2x)-4=13`?

Answer 1

Please see the explanation.

Explanation:

Add 4 to both sides:

`5(2)^(2x) = 17`

Divide both sides by 5:

`(2)^(2x) = 17/5`

Use the natural logarithm on both sides:

`ln((2)^(2x)) = ln(17/5)`

Use the property `ln(a^b) = (b)ln(a)`

`(2x)ln((2)) = ln(17/5)`

Divide both sides by 2ln(x):

`x = ln(17/5)/(2ln(2))`

check:

`5(2)^(2(ln(17/5)/(2ln(2)))) - 4 = 13`

`5(2)^((ln(17/5)/(ln(2)))) - 4 = 13`

`5(2)^((log_2(17/5)) - 4 = 13`

`5(17/5) - 4 = 13`

`17 - 4 = 13`

`13 = 13`

`x = ln(17/5)/(2ln(2))` checks.