Webwork

Logarithmic Functions – Equations: Problem 6

solve for x: log5(x+14)-log5(x+6)=3

1. First combine the log5 since they both have the same base and we want to make them one log equation. Since they are subtracted then we need to combine them with division.

log5(x+14/x+6)=3

2. Afterward then we turn the equation into the exponent

5^3=(x+14/x+6)

3. Then we solve the exponent and multiply the denominator

125(x+6)=(x+14)

4. Distribute the constants

125x+750=x+14

5. Afterward then isolate the variable-x

x=-736/124

6. After you can simplify the fraction

x=-184/31

P.S: Sorry for any errors