log4(-7z+127)=3

Rewrite log4(-7z+127)=3 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then logb(x)=y is equivalent to by=x.

43=-7z+127

Raise 4 to the power of 3.

64=-7z+127

Rewrite the equation as -7z+127=64.

-7z+127=64

Move all terms not containing z to the right side of the equation.

Subtract 127 from both sides of the equation.

-7z=64-127

Subtract 127 from 64.

-7z=-63

-7z=-63

Divide each term by -7 and simplify.

Divide each term in -7z=-63 by -7.

-7z-7=-63-7

Cancel the common factor of -7.

Cancel the common factor.

-7z-7=-63-7

Divide z by 1.

z=-63-7

z=-63-7

Divide -63 by -7.

z=9

z=9

z=9

Solve for z log base 4 of -7z+127=3