What is log_{10}((R^5S^4)/(2^6)) ?

The solution to log_{10}((R^5S^4)/(2^6)) is 5log_{10}(R)+4log_{10}(S)-6log_{10}(2)

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simplify log_{10}((R^5S^4)/(2^6))

simplify

lo g_{10} (\frac{R ^{5} S ^{4}}{2 ^{6}})

5 lo g_{10} (R) + 4 lo g_{10} (S) - 6 lo g_{10} (2)

Solution steps

lo g_{10} (\frac{R ^{5} S ^{4}}{2 ^{6}})

Simplify

\frac{R ^{5} S ^{4}}{2 ^{6}} : \frac{R ^{5} S ^{4}}{64}

= lo g_{10} (\frac{R ^{5} S ^{4}}{64})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{R ^{5} S ^{4}}{64}) = lo g_{10} (R^{5} S^{4}) - lo g_{10} (64)

= lo g_{10} (R^{5} S^{4}) - lo g_{10} (64)

lo g_{10} (R^{5} S^{4}) = 5 lo g_{10} (R) + 4 lo g_{10} (S)

lo g_{10} (64) = 6 lo g_{10} (2)

= 5 lo g_{10} (R) + 4 lo g_{10} (S) - 6 lo g_{10} (2)

ln (y) + ln (4)

lo g_{10} (a) + 3 lo g_{10} (b) - 3

lo g_{3} (2 x) - 5 lo g_{3} (y)

- lo g_{10} (2 \times 1 0^{- 5})

What is log_{10}((R^5S^4)/(2^6)) ?
The solution to log_{10}((R^5S^4)/(2^6)) is 5log_{10}(R)+4log_{10}(S)-6log_{10}(2)