1. ## Write the expression

Write the expression LoGa(y+5)+2loga(x+1) as one logarithm. My answer is loga(y+2x+7), but not sure if thats right. thanks for looking.

2. Hello, kwtolley!

Write the expression $\log_a(y+5) + 2\log_a(x+1)$ as one logarithm.

My answer is: $\log_a(y+2x+7)$, but not sure if thats right.

You're expected to know the three Properties of Logarithms:
. . $[1]\;\log_b(XY) \:= \:\log_b(X) + \log_b(Y)$
. . $[2]\;\log_b\left(\frac{X}{Y}\right) \:=\:\log_b(X) - \log_b(Y)$
. . $[3]\;\log_b\left(X^n\right) \:= \:n\cdot\log_b(X)$

So we have: . $\log_a(y+5) + 2\log_a(x+1)$

. . . . . . . . $= \;\log_a(y+5) + \log_a(x+1)^2$ . . . property [3]

. . . . . . . . $= \;\log_a\left[(y+5)(x+1)^2\right]$ . . . property [1]