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Question
Find the value of x, if `5^(x - 3) xx 5^(2x – 8)` = 625.
Solution
Given: `5^(x - 3) xx 5^(2x – 8)` = 625.
⇒ `5^(x - 3) xx 5^(2x – 8)` = 54
We know that if the basis is the same, then powers will be added.
∴ `5^((x - 3) + (2x – 8))` = 54
`5^(3x - 11)` = 54
We get by equating the exponents
3x – 11 = 4
⇒ 3x = 4 + 11
⇒ 3x = 15
⇒ x = 5
As a result, the value of x is 5.
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