Solve the following equation:
log105 + log10(5x + 1) = log10(x + 5) + 1
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Given,
⇒ log105 + log10(5x + 1) = log10(x + 5) + 1
⇒ log105(5x + 1) = log10(x + 5) + log1010
⇒ log10(25x + 5) = log1010(x + 5)
⇒ log10(25x + 5) = log10(10x + 50)
⇒ 25x + 5 = 10x + 50
⇒ 25x - 10x = 50 - 5
⇒ 15x = 45
⇒ x = 3.
Hence, x = 3.
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log(x + 1) + log(x - 1) = log 24
log(10x + 5) - log(x - 4) = 2
log(4y - 3) = log(2y + 1) - log 3
log10(x + 2) + log10(x - 2) = log103 + 3log104