Question 177(vi)

Find x.

$5^{x} + 5^{x - 1} = 750$

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Solution

$5^{x} + 5^{x - 1} = 750 \Rightarrow 5^{x} + \frac{5^{x}}{5} = 750 \Rightarrow 5^{x} (1 + \frac{1}{5}) = 750 \Rightarrow 5^{x} (\frac{6}{5}) = 750 \Rightarrow 5^{x} = 750 \times \frac{5}{6} \Rightarrow 5^{x} = 125 \times 5 \Rightarrow 5^{x} = 5^{3} \times 5 \Rightarrow 5^{x} = 5^{4}$
Since the base are same on both sides, we can equate the powers.
On equating the powers of 5, we get
x = 4

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