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If $$5^{3x-1}\div 25=125$$, find the value of $$x$$.
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## QuestionMathsClass 8

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

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 $$2$$.