# Solve for x 0.125*4^(2x-8)=(0.25÷( square root of 2))^(-x)

0.125⋅42x-8=(0.25÷2)-x
Rewrite the division as a fraction.
0.125⋅42x-8=(0.252)-x
Multiply 0.252 by 22.
0.125⋅42x-8=(0.252⋅22)-x
Combine and simplify the denominator.
Multiply 0.252 and 22.
0.125⋅42x-8=(0.25222)-x
Raise 2 to the power of 1.
0.125⋅42x-8=(0.252212)-x
Raise 2 to the power of 1.
0.125⋅42x-8=(0.2522121)-x
Use the power rule aman=am+n to combine exponents.
0.125⋅42x-8=(0.25221+1)-x
0.125⋅42x-8=(0.25222)-x
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
0.125⋅42x-8=(0.252(212)2)-x
Apply the power rule and multiply exponents, (am)n=amn.
0.125⋅42x-8=(0.252212⋅2)-x
Combine 12 and 2.
0.125⋅42x-8=(0.252222)-x
Cancel the common factor of 2.
Cancel the common factor.
0.125⋅42x-8=(0.252222)-x
Divide 1 by 1.
0.125⋅42x-8=(0.25221)-x
0.125⋅42x-8=(0.25221)-x
Evaluate the exponent.
0.125⋅42x-8=(0.2522)-x
0.125⋅42x-8=(0.2522)-x
0.125⋅42x-8=(0.2522)-x
Multiply 0.25 by 2.
0.125⋅42x-8=(0.353553392)-x
Divide 0.35355339 by 2.
0.125⋅42x-8=0.17677669-x
Subtract 0.17677669-x from both sides of the equation.
0.125⋅42x-8-0.17677669-x=0
Factor 0.125 out of 0.125⋅42x-8-0.17677669-x.
Factor 0.125 out of 0.125⋅42x-8.
0.125(42x-8)-0.17677669-x=0
Factor 0.125 out of -0.17677669-x.
0.125(42x-8)+0.125(-8⋅0.17677669-x)=0
Factor 0.125 out of 0.125(42x-8)+0.125(-8⋅0.17677669-x).
0.125(42x-8-8⋅0.17677669-x)=0
0.125(42x-8-8⋅0.17677669-x)=0
Divide each term by 0.125 and simplify.
Divide each term in 0.125(42x-8-8⋅0.17677669-x)=0 by 0.125.
0.125(42x-8-8⋅0.17677669-x)0.125=00.125
Cancel the common factor of 0.125.
42x-8-8⋅0.17677669-x=00.125
Divide 0 by 0.125.
42x-8-8⋅0.17677669-x=0
42x-8-8⋅0.17677669-x=0
Factor the exponential expression.
(0.17677669-x)((0.17677669-x)+0.17677669-x)=0
0.17677669-x(2⋅0.17677669-x)=0
Set the factor of 2⋅0.17677669-x equal to 0 and solve for x.
2⋅0.17677669-x=0
Solve for x.
Divide each term by 2 and simplify.
Divide each term in 2⋅0.17677669-x=0 by 2.
2⋅0.17677669-x2=02
Cancel the common factor of 2.
Cancel the common factor.
2⋅0.17677669-x2=02
Divide 0.17677669-x by 1.
0.17677669-x=02
0.17677669-x=02
Divide 0 by 2.
0.17677669-x=0
0.17677669-x=0
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(0.17677669-x)=ln(0)
The equation cannot be solved because ln(0) is undefined.
Undefined
There is no solution for 0.17677669-x=0
No solution
No solution
Solve for x 0.125*4^(2x-8)=(0.25÷( square root of 2))^(-x)