# Solve for y 10^(4 log of y)=16

104log(y)=16
Simplify the left side.
Simplify 4log(y) by moving 4 inside the logarithm.
10log(y4)=16
Exponentiation and log are inverse functions.
y4=16
y4=16
Take the 4th root of both sides of the equation to eliminate the exponent on the left side.
y=±164
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 16 as 24.
y=±244
Pull terms out from under the radical, assuming positive real numbers.
y=±2
y=±2
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=2
Next, use the negative value of the ± to find the second solution.
y=-2
The complete solution is the result of both the positive and negative portions of the solution.
y=2,-2
y=2,-2
y=2,-2
Exclude the solutions that do not make 104log(y)=16 true.
y=2
Solve for y 10^(4 log of y)=16

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