Question
$5^x+ 5^{x-1}= 750$
✓
Answer
$5\text{x} + 5\text{x}–1 = 750$
$\Rightarrow \ 5^{\text{x}}+\frac{5\text{x}}{5}=750$ $\Big[\because\text{a}^{\text{-m}}=\frac{1}{\text{a}^{\text{m}}}\Big]$
$\Rightarrow \ 5^{\text{x}}\Big(1+\frac{1}{5}\Big)=750 $
$\Rightarrow \ 5^\text{x}\Big(\frac{6}{5}\Big)=750 $
$\Rightarrow \ 5^{\text{x}}=750\times\frac{5}{6}$ $\Rightarrow \ 5^{\text{x}}=125\times5$ $\Rightarrow \ 5^{\text{x}}=625$
$\Rightarrow \ 5^{\text{x}}=5^4$
On compairing the powers of $5,$
$$we get $\text{x} = 4$
$\Rightarrow \ 5^{\text{x}}+\frac{5\text{x}}{5}=750$ $\Big[\because\text{a}^{\text{-m}}=\frac{1}{\text{a}^{\text{m}}}\Big]$
$\Rightarrow \ 5^{\text{x}}\Big(1+\frac{1}{5}\Big)=750 $
$\Rightarrow \ 5^\text{x}\Big(\frac{6}{5}\Big)=750 $
$\Rightarrow \ 5^{\text{x}}=750\times\frac{5}{6}$ $\Rightarrow \ 5^{\text{x}}=125\times5$ $\Rightarrow \ 5^{\text{x}}=625$
$\Rightarrow \ 5^{\text{x}}=5^4$
On compairing the powers of $5,$
$$we get $\text{x} = 4$
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