Solve for x 3^(x-5)=7^(2x)

Problem

3(x−5)=7(2*x)

Solution

1. Take the natural logarithm of both sides of the equation to move the variables out of the exponents.

ln(3(x−5))=ln(7(2*x))

2. Apply the power rule for logarithms, ln(ab)=b*ln(a) to both sides.

(x−5)*ln(3)=2*x*ln(7)

3. Distribute the constant ln(3) into the parentheses.

x*ln(3)−5*ln(3)=2*x*ln(7)

4. Isolate the terms containing x on one side of the equation by subtracting 2*x*ln(7) and adding 5*ln(3)

x*ln(3)−2*x*ln(7)=5*ln(3)

5. Factor out the common factor x from the left side.

x*(ln(3)−2*ln(7))=5*ln(3)

6. Solve for x by dividing both sides by the expression in the parentheses.

x=(5*ln(3))/(ln(3)−2*ln(7))

7. Simplify the denominator using the power rule 2*ln(7)=ln(7)=ln(49)

x=(5*ln(3))/(ln(3)−ln(49))

Final Answer

x=(5*ln(3))/(ln(3)−ln(49))

Want more problems? Check here!