How would I evaluate this logarithm

[Jen123]

Evaluate: (log₅ (20⁴))(log₂₀ (5⁴))

I couldn't find any examples in an algebra book or an advanced math book so could someone please help me solve this problem!
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Edited by stapel --- Reason for edit: making subscripts visible

 

[soroban]

Hello, Jen!

Evaluate : \(\displaystyle \:\log_5\left(20^4\right)\,\cdot\,\log_{20}\left(5^4\right)\)

We're expected to know this identity: \(\displaystyle \:\log_b(a) \:=\:\frac{1}{\log_a(b)}\)


We have: \(\displaystyle \:\left[4\cdot\log_5(20)\right]\,\cdot\,\left[4\cdot\log_{20}(5)\right]\)

. . . . . . . . . . . . . . . . . . . . . \(\displaystyle {\color{red}\downarrow}\)

. . . . . . \(\displaystyle =\;\left[4\cdot\log_5(20)\right]\,\cdot\,\left[4\cdot\frac{1}{\log_5(20)}\right] \;=\;4\,\cdot\,4 \;=\;\fbox{16}\)