Answer:
[tex]6[/tex]
Step-by-step explanation:
[tex]\log _3\left(27\right)+\log _2\left(8\right)\\\log _3\left(27\right)=3\\\log _3\left(27\right)\\\mathrm{Rewrite\:}27\mathrm{\:in\:power-base\:form:}\quad 27=3^3\\=\log _3\left(3^3\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _3\left(3^3\right)=3\log _3\left(3\right)\\=3\log _3\left(3\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\log _3\left(3\right)=1\\=3\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:3\cdot \:1=3\\=3[/tex]
[tex]\log _2\left(8\right)=3\\\log _2\left(8\right)\\\mathrm{Rewrite\:}8\mathrm{\:in\:power-base\:form:}\quad 8=2^3\\=\log _2\left(2^3\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _2\left(2^3\right)=3\log _2\left(2\right)\\=3\log _2\left(2\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\log _2\left(2\right)=1\\=3\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:3\cdot \:1=\\=3\\=3+3\\Simplify\\=6[/tex]
