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# 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

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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

Apr 19, 2015

#1
+17747
+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

Apr 20, 2015

#1
+17747
+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