Write the expression as a single logarithm.
$2 (\log_{4} w - 4 \log_{4} y) + 2 \log_{4} z$

Answer

Expert–verified

Hide Steps

Answer

The final answer is $\log_{4} (\frac{w^{2} z^{2}}{y^{8}})$

Steps

Step 1 ：The given expression is $2 (\log_{4} w - 4 \log_{4} y) + 2 \log_{4} z$

Step 2 ：We can simplify it by using the properties of logarithms. The properties we will use are: $\log_{b} (a^{n}) = n * \log_{b} (a)$ , $\log_{b} (a) - \log_{b} (b) = \log_{b} (a / b)$ , and $\log_{b} (a) + \log_{b} (b) = \log_{b} (a b)$

Step 3 ：Applying these properties to the given expression, we get $\log (w^{2}) / \log (4) - 8 * \log (y) / \log (4) + 2 * \log (z) / \log (4)$

Step 4 ：Simplifying further, we get $\log (w^{2} * z^{2} / y^{8}) / \log (4)$

Step 5 ：The final answer is $\log_{4} (\frac{w^{2} z^{2}}{y^{8}})$

Write the expression as a single logarithm.2(log4⁡w−4log4⁡y)+2log4⁡z

Answer

Popular Problems

Write the expression as a single logarithm.
$2 (\log_{4} w - 4 \log_{4} y) + 2 \log_{4} z$