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
