What is log_{10}(48)+log_{10}(6)-log_{10}(108) ?

The solution to log_{10}(48)+log_{10}(6)-log_{10}(108) is log_{10}(8/3)

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simplify log_{10}(48)+log_{10}(6)-log_{10}(108)

simplify

lo g_{10} (48) + lo g_{10} (6) - lo g_{10} (108)

lo g_{10} (\frac{8}{3})

Decimal Notation

0.42596 \dots

Solution steps

lo g_{10} (48) + lo g_{10} (6) - lo g_{10} (108)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (48) + lo g_{10} (6) = lo g_{10} (48 \cdot 6)

= lo g_{10} (48 \cdot 6) - lo g_{10} (108)

48 \cdot 6 = 288

= lo g_{10} (288) - lo g_{10} (108)

Apply log rule:

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

lo g_{10} (288) - lo g_{10} (108) = lo g_{10} (\frac{288}{108})

= lo g_{10} (\frac{288}{108})

Cancel

\frac{288}{108} : \frac{8}{3}

= lo g_{10} (\frac{8}{3})

lo g_{7} (3 x + 1) - 2 lo g_{7} (1 + x)

2 ln (x + 49) - 4 ln (x - 7)

ln (x - 5) + ln (x + 5)

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

lo g_{b} (x^{2} y)

What is log_{10}(48)+log_{10}(6)-log_{10}(108) ?
The solution to log_{10}(48)+log_{10}(6)-log_{10}(108) is log_{10}(8/3)