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If \(5^{3x-1}\div 25=125\), find the value of \(x\).
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Question

If \(5^{3x-1}\div 25=125\), find the value of \(x\).

Answer

Given, \(5^{3x-1}\div 25=125\).
\(\Rightarrow\) \(\frac{5^{3x-1}}{ 25}=125\)
\(\Rightarrow\) \(5^{3x-1}=125\times25\) [By cross multiplication]
\(\Rightarrow\) \(5^{3x-1}=5^3\times5^2\)
\(\Rightarrow\) \(5^{3x-1}=5^5\) \([\because a^m\times a^n=a^{m+n}]\)
Now, comparing the powers of \(5\), we get,
\(3x-1=5\)
\(\Rightarrow\) \(3x=5+1\)
\(\Rightarrow\) \(3x=6\)
\(\Rightarrow\) \(x=\frac{6}{3}\)
\(\Rightarrow\) \(x=2\)
Hence, the value of \(x\) is \(2\).
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