How can I isolate x to the left side of the equation to solve for x the following: 10^(-0.627 * log(x) + 0.07233) = 25.5
10-0.627 log(x) + 0.07233 = 25.5
Find the log of both sides:
log( 10-0.627 log(x) + 0.07233 ) = log( 25.5 )
Since exponents come out of logs as multipliers:
( -0.627 log(x) + 0.07233 ) log(10) = log(25.5)
Since log(10) = 1:
-0.627 log(x) + 0.07233 = log(25.5)
Subtract 0.07233 from both sides:
-0.627 log(x) = log(25.5) - 0.07233
Divide both sides by -0.627:
log(x) = [ log(25.5) - 0.07233 ] / -0.627
Write into exponential form:
x = 10[ log(25.5) - 0.07233 ] / -0.627
10-0.627 log(x) + 0.07233 = 25.5
Find the log of both sides:
log( 10-0.627 log(x) + 0.07233 ) = log( 25.5 )
Since exponents come out of logs as multipliers:
( -0.627 log(x) + 0.07233 ) log(10) = log(25.5)
Since log(10) = 1:
-0.627 log(x) + 0.07233 = log(25.5)
Subtract 0.07233 from both sides:
-0.627 log(x) = log(25.5) - 0.07233
Divide both sides by -0.627:
log(x) = [ log(25.5) - 0.07233 ] / -0.627
Write into exponential form:
x = 10[ log(25.5) - 0.07233 ] / -0.627