Solve for x 8^x=16

Problem

8^x=16

Solution

1. Identify a common base for both sides of the equation. Both 8 and 16 are powers of 2

2. Rewrite the numbers using the base 2 Since 8=2^3 and 16=2^4 the equation becomes:

(2^3)^x=2^4

3. Apply the power of a power rule, which states (a^m)^n=a^(m⋅n) to simplify the left side:

2^(3*x)=2^4

4. Equate the exponents because the bases are now identical:

3*x=4

5. Solve for x by dividing both sides of the equation by 3

x=4/3

Final Answer

8^x=16⇒x=4/3

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