What is log_{10}(6)(k^2-36)-log_{10}(6k)-6 ?

The solution to log_{10}(6)(k^2-36)-log_{10}(6k)-6 is log_{10}((6^{k^2-37})/k)-6

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simplify log_{10}(6)(k^2-36)-log_{10}(6k)-6

simplify

lo g_{10} (6) (k^{2} - 36) - lo g_{10} (6 k) - 6

lo g_{10} (\frac{6 ^{k^{2} - 37}}{k}) - 6

Solution steps

lo g_{10} (6) (k^{2} - 36) - lo g_{10} (6 k) - 6

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

lo g_{10} (6) (k^{2} - 36) = lo g_{10} (6^{k^{2} - 36})

= lo g_{10} (6^{k^{2} - 36}) - lo g_{10} (6 k) - 6

Simplify

lo g_{10} (6^{k^{2} - 36}) - lo g_{10} (6 k) : lo g_{10} (\frac{6 ^{k^{2} - 37}}{k})

= lo g_{10} (\frac{6 ^{k^{2} - 37}}{k}) - 6

lo g_{10} (z) - lo g_{10} (2 y)

\frac{1}{2} lo g_{10} (2 x) - \frac{5}{2} lo g_{10} (y)

2 ln (x - 1) + 3 ln (4) - ln (x)

ln (2 \cdot x)

2 π + 16 ln (\frac{2}{2})

What is log_{10}(6)(k^2-36)-log_{10}(6k)-6 ?
The solution to log_{10}(6)(k^2-36)-log_{10}(6k)-6 is log_{10}((6^{k^2-37})/k)-6