Question

Use the properties of logarithms to rewrite the expression.log7(8x+9y)a. log7(8x+9y)(log7 8x) (log7 9y)log7 8x + log7 9ylog7 72xy

Answer 1

we have this expression

`\log 7\cdot(8x+9y)`

applying the properties of the logarithms, we get

`\begin{gathered} \log _(10)\mleft(7\mright)\mleft(8x+9y\mright) \\ a\mleft(b+c\mright)=ab+ac;a=\log _(10)\mleft(7\mright),\: b=8x,\: c=9y \\ =\log _(10)\mleft(7\mright)\cdot\: 8x+\log _(10)\mleft(7\mright)\cdot\: 9y \\ =8\log _(10)\mleft(7\mright)x+9\log _(10)\mleft(7\mright)y \end{gathered}`

then the answer would be

log7 8x + log7 9y