Question

Please show ALL work!!!!

Answer 1

Answer:

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

Step-by-step 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:

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

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

Answer 2

Answer


I only know how to get the answer but not explain