solve the exponential equation
5(2)^2x - 4 = 13 thanks
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