Solve for x 3(5^(x-1))=21

Problem

3*(5(x−1))=21

Solution

1. Isolate the exponential term by dividing both sides of the equation by 3

5(x−1)=21/3

5(x−1)=7

2. Apply the logarithm to both sides to move the variable out of the exponent. We will use the natural logarithm ln()

ln(5(x−1))=ln(7)

3. Use the power rule of logarithms, which states ln(ab)=b*ln(a) to bring down the exponent.

(x−1)*ln(5)=ln(7)

4. Solve for x by first dividing by ln(5) and then adding 1 to both sides.

x−1=ln(7)/ln(5)

x=ln(7)/ln(5)+1

Final Answer

x=ln(7)/ln(5)+1

Want more problems? Check here!