solve the exponential equation

Question

5(2)^2x - 4 = 13 thanks

Answer 1

If 5(2)^2x - 4 = 13 mean

5 * [ 2 ^ ( 2 x ) ] - 4 = 13

then

5 * 2 ^ 2 x - 4 = 13

5 * 2 ^ 2 x = 13 + 4

5 * 2 ^ 2 x = 17 Divide both sides by 5

2 ^ 2 x = 17 / 5

2 x * log ( 2 ) = log ( 17 / 5 )

2 x * log ( 2 ) = log ( 17 ) - log ( 5 ) Divide both sides by 2 log ( 2)

x = [ log ( 17 ) - log ( 5 ) ] / 2 log ( 2 )

Remark:

log ( a / b ) = log ( a) - log ( b )

log ( 17 / 5 ) = log ( 17 ) - log ( 5 )

x = 0.88276737

2 x = 1.76553474

5 * 2 ^ 1.76553474 - 4 =

5 * 3.4 - 4 =

17 - 4 = 13