Solve logx 164 32Solutionlogx 164 3x use the property logx

Solve: logx 1/64 = 3/2

logx( 1/64) = 3/x

use the property: logx^a = alogx

So, logx(1/2)^6 = 3/2

6*logx(1/2) = 3/2

logx(1/2) = 1/4

Now . (1/2) = x^1/4

take log on both sides:

log(1/2) = (1/4) logx

logx = log(1/2)/1/4 = 4log(1/2)

logx = log(1/2)^4

x = (1/2)^4

x = 1/16