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Question
If 5x + 1 = 25x - 2, find the value of 3x - 3 × 23 - x.
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Solution
5x + 1 = 25x - 2
⇒ 5x + 1 = (52)x - 2
⇒ 5x + 1 = 52x - 4
If bases are equal, powers are also equal.
⇒ x + 1 = 2x - 4
⇒ 2x - x = 4 + 1
⇒ x = 5
∴ 3x - 3 x 23 - x
= 35 - 3 x 23 - 5
= 32 x 2-2
= 9 x `1/4 = 9/4`
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