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.
Hello, kwtolley!
Write the expression $\displaystyle \log_a(y+5) + 2\log_a(x+1)$ as one logarithm.
My answer is: $\displaystyle \log_a(y+2x+7)$, but not sure if thats right.
You're expected to know the three Properties of Logarithms:
. . $\displaystyle [1]\;\log_b(XY) \:= \:\log_b(X) + \log_b(Y)$
. . $\displaystyle [2]\;\log_b\left(\frac{X}{Y}\right) \:=\:\log_b(X) - \log_b(Y)$
. . $\displaystyle [3]\;\log_b\left(X^n\right) \:= \:n\cdot\log_b(X)$
So we have: .$\displaystyle \log_a(y+5) + 2\log_a(x+1)$
. . . . . . . .$\displaystyle = \;\log_a(y+5) + \log_a(x+1)^2$ . . . property [3]
. . . . . . . .$\displaystyle = \;\log_a\left[(y+5)(x+1)^2\right]$ . . . property [1]