104log(y)=16

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

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