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

Guest Apr 19, 2015

#1**+8 **

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}

geno3141
Apr 20, 2015

#1**+8 **

Best Answer

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}

geno3141
Apr 20, 2015