Solve for x 6(5^x)=7

Problem

6*(5)=7

Solution

1. Isolate the exponential term by dividing both sides of the equation by 6

5=7/6

2. Apply the natural logarithm to both sides to bring the variable x out of the exponent.

ln(5)=ln(7/6)

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

x*ln(5)=ln(7/6)

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

x=ln(7/6)/ln(5)

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

x=(ln(7)−ln(6))/ln(5)

Final Answer

x=(ln(7)−ln(6))/ln(5)

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