What is log_{10}(5 6/(x^7)) ?

The solution to log_{10}(5 6/(x^7)) is 1+log_{10}(3)-7log_{10}(x)

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simplify log_{10}(5 6/(x^7))

simplify

lo g_{10} (5 \frac{6}{x ^{7}})

1 + lo g_{10} (3) - 7 lo g_{10} (x)

Solution steps

lo g_{10} (5 \cdot \frac{6}{x ^{7}})

Simplify

5 \cdot \frac{6}{x ^{7}} : \frac{30}{x ^{7}}

= lo g_{10} (\frac{30}{x ^{7}})

Apply log rule:

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

lo g_{10} (\frac{30}{x ^{7}}) = lo g_{10} (30) - lo g_{10} (x^{7})

= lo g_{10} (30) - lo g_{10} (x^{7})

lo g_{10} (30) = 1 + lo g_{10} (3)

lo g_{10} (x^{7}) = 7 lo g_{10} (x)

= 1 + lo g_{10} (3) - 7 lo g_{10} (x)

lo g_{5} (\frac{25 b ^{5} y ^{2} - 1}{y ( x + 1 ) ^{2}})

ln (\frac{1}{e ^{8}}) + ln (8) e^{3}

ln (x^{6}) - 2 ln (x^{3})

2 ln (3) + ln (4)

lo g_{4} (5) - lo g_{4} (11)

What is log_{10}(5 6/(x^7)) ?
The solution to log_{10}(5 6/(x^7)) is 1+log_{10}(3)-7log_{10}(x)