Answer:
[tex]=8[/tex]
Step-by-step explanation:
[tex]\log _2\left(16\right)\log _3\left(9\right)\\\mathrm{Simplify}\:\log _2\left(16\right):\quad 4\\\log _2\left(16\right)\\\mathrm{Rewrite\:}16\mathrm{\:in\:power-base\:form:}\quad 16=2^4\\=\log _2\left(2^4\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _2\left(2^4\right)=4\log _2\left(2\right)\\=4\log _2\left(2\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\log _2\left(2\right)=1\\=4\cdot \:1[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1=4\\=4\\=4\log _3\left(9\right)\\\mathrm{Simplify}\:\log _3\left(9\right):\quad 2\\\log _3\left(9\right)\\\mathrm{Rewrite\:}9\mathrm{\:in\:power-base\:form:}\quad 9=3^2\\=\log _3\left(3^2\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _3\left(3^2\right)=2\log _3\left(3\right)\\=2\log _3\left(3\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\log _3\left(3\right)=1\\=2\cdot \:1[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2\\=2\\=4\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=8[/tex]
