Question

Please show ALL work!!!!

Answer 1

Answer


I only know how to get the answer but not explain

Answer 2

`$\boxed{\log _2\left((zx^2)/(y^2) \right) +\log _9(y^4 x^(12))} $`

Explanation:

`\log _2z+2\log _2x+4\log _9y+12\log _9x-2\log _2y`

We have logarithms in base 2 and 9. Let's rewrite it:

`\log _2z+2\log _2x-2\log _2y+4\log _9y+12\log _9x`

Remember that:

`\boxed{p\log _bc=\log _b c^p}`

`\log _2z+\log _2 x^2 -\log _2y^2 +\log _9y^4+\log _9x^(12)`

Remember the Product Rule:

`\boxed{\log_b(xy)=\log_bx + \log_by}`

`\log _2(zx^2) -\log _2y^2 +\log _9(y^4 x^(12))`

Finally, remember the Quotient Rule:

`$\boxed{\log_b\left((x)/(y) \right)=\log_bx - \log_by}$`

`$\log _2\left((zx^2)/(y^2) \right) +\log _9(y^4 x^(12))$`