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Question: If \(\log_{5}a.\log_{a}x = 2,\) then x is equal to...

If log⁡5a.log⁡ax=2,\log_{5}a.\log_{a}x = 2, then x is equal to

A

125

B

a2a^{2}

C

25

D

None of these

Answer

25

Explanation

Solution

log⁡5a.log⁡ax=2⇒\log_{5}a.\log_{a}x = 2 \Rightarrow =log⁡ealog⁡eb×log⁡eblog⁡ec×log⁡eclog⁡ea=1⇒x=52=25= \frac{\log_{e}a}{\log_{e}b} \times \frac{\log_{e}b}{\log_{e}c} \times \frac{\log_{e}c}{\log_{e}a} = 1 \Rightarrow x = 5^{2} = 25.