Math(alg2)
posted by Sammy on .
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