Answer:
2+x
Explanation:
Given the following:
[tex]\begin{gathered} \log _25=x \\ \log _23=y \end{gathered}[/tex]
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
[tex]\begin{gathered} \log _220=\log _2(4\times5) \\ =\log _2(2^2\times5) \end{gathered}[/tex]
Next, since we have the multiplication sign, we use the addition law:
[tex]=\log _22^2+\log _25[/tex]
The power of the number becomes the product of the log, so we have:
[tex]=2\log _22+\log _25[/tex]
When you have the same base and number, the result is always 1.
[tex]\begin{gathered} \log _22=1 \\ \implies2\log _22+\log _25=2(1)+\log _25 \\ =2+x \end{gathered}[/tex]
Therefore:
[tex]\text{log}_220=2+x[/tex]
