Solve for x 2(5^x)=32

Problem

2*(5)=32

Solution

1. Isolate the exponential term by dividing both sides of the equation by 2

5=32/2

5=16

2. Apply the natural logarithm to both sides to bring the variable down from the exponent.

ln(5)=ln(16)

3. Use the power rule of logarithms, ln(ab)=b*ln(a) to move the x to the front.

x*ln(5)=ln(16)

4. Solve for x by dividing both sides by ln(5)

x=ln(16)/ln(5)

5. Simplify the expression if desired by noting that 16=2

x=ln(2)/ln(5)

x=(4*ln(2))/ln(5)

Final Answer

x=ln(16)/ln(5)

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