Question

Given that logof 2 to the base 10= x and log of 3 to the base 10 = y, the value of log of 60 to the base 10 is expressed as
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Answer 1

Answer:

$log_{10}(2) = x \\ i.e \: {10}^{x} = 2.........(1) \\ log_{10}(3) = y \\ i.e \: {10}^{y} = 3 \: .......(2) \: \\ now \: (1) \times (2) \\ \\ {10}^{x} \times {10}^{y} = 3 \times 2 \\ {10}^{x + y} = 6 \: \: \: \: \\ now \: multiply \: both \: sides \: with \: 10 \\i .e \: \: {10}^{x + y} \times 10 = 6 \times 10 \\ {10}^{x + y + 1} = 60 \\ log_{10}(60) = x + y + 1 \\ hope \: it \: may \: help \: u$