Solve for x 4^x=32

Problem

4^x=32

Solution

1. Rewrite both sides of the equation using a common base. Since 4=2^2 and 32=2^5 we can express both sides as powers of 2

(2^2)^x=2^5

2. Apply the power of a power rule, which states that (a^m)^n=a^(m*n) to the left side of the equation.

2^(2*x)=2^5

3. Equate the exponents because the bases are now identical.

2*x=5

4. Solve for x by dividing both sides of the equation by 2

x=5/2

Final Answer

4^x=32⇒x=5/2

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