Solve for x 5(3^x)=7

Problem

5*(3^x)=7

Solution

1. Isolate the exponential term by dividing both sides of the equation by 5

3^x=7/5

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

ln(3^x)=ln(7/5)

3. Use the power rule for logarithms, which states ln(a^b)=b*ln(a) to move x in front of the logarithm.

x*ln(3)=ln(7/5)

4. Solve for x by dividing both sides by ln(3)

x=ln(7/5)/ln(3)

5. Apply the quotient rule for logarithms, ln(a/b)=ln(a)−ln(b) to simplify the numerator.

x=(ln(7)−ln(5))/ln(3)

Final Answer

x=(ln(7)−ln(5))/ln(3)

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