Using laws of logarithms, write the expression below as a single logarithm 6(log(x+2)+(⁷⁄₆)log(x+1))= log(________________)

Question

Please help me with this. No one can figure it out.

Answer 1

You have to use logarithm properties to combine the logarithms together. When there is a coefficient in front of a logarithm, you make it a power. When you add two logarithms together, you multiply the insides together. So the final answer becomes:

log(((x+2)(x+1)^(7/6))^6)

Answer 2

Try distributing the 6 first to get:

6log(x+2)+7log(x+1)

Now use the power property of logs to get:

log(x+2)⁶+log(x+1)⁷

Finally the fact that the log of a product equals the sum of the logs:

log[(x+2)⁶(x+1)⁷]

Check out this Desmos graph for confirmation:

desmos.com/calculator/ewlqzw1uur