Question 82643
*[Tex \Large \log_a{y+5}+2\log_a{x+1}] Start with the given expression


*[Tex \Large \log_a({y+5})+\log_a({x+1})^{2}] Use the identity *[Tex \Large y\log_a({x})=\log_a({x})^{y}] to move the 2 to the exponent


*[Tex \Large \log_a({y+5})+\log_a({x^2+2x+1})] Foil {{{(x+1)^2}}}


*[Tex \Large \log_a(y+5)(x^2+2x+1)] Combine the logs using this identity *[Tex \Large \log_a({x})+\log_a({y})=\log_a({xy})]


*[Tex \Large \log_a(x^2y+2xy+y+5x^2+10x+5)] Multiply the terms out