Solve for x 2^x*8^(-x)=4^x

Problem

2⋅8(−x)=4

Solution

1. Rewrite all terms using a common base of 2

8=2

4=2

2. Substitute these values into the original equation.

2⋅(2)(−x)=(2)x

3. Apply the power of a power rule, which states (am)n=a(m*n)

2⋅2(−3*x)=2(2*x)

4. Apply the product rule for exponents, which states am⋅an=a(m+n) to the left side.

2(x−3*x)=2(2*x)

2(−2*x)=2(2*x)

5. Equate the exponents since the bases are equal.

−2*x=2*x

6. Solve for x by moving all terms to one side.

0=4*x

x=0

Final Answer

2⋅8(−x)=4⇒x=0

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