Solve for x 36(1/3)^(x/5)=4

Problem

36*(1/3)x/5=4

Solution

1. Isolate the exponential term by dividing both sides of the equation by 36

(1/3)x/5=4/36

2. Simplify the fraction on the right side of the equation.

(1/3)x/5=1/9

3. Rewrite the right side as a power with a base of 1/3 to match the left side.

(1/3)x/5=(1/3)2

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

x/5=2

5. Solve for x by multiplying both sides of the equation by 5

x=10

Final Answer

x=10

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