Solve for x 27^x=81

Problem

27=81

Solution

1. Identify the common base for both sides of the equation. Both 27 and 81 are powers of 3

2. Rewrite the numbers using the base 3

27=3

81=3

3. Substitute these expressions back into the original equation.

(3)x=3

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

3(3*x)=3

5. Equate the exponents since the bases are now identical.

3*x=4

6. Solve for x by dividing both sides by 3

x=4/3

Final Answer

x=4/3

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