What is log_{10}(48)+log_{10}(75) ?

The solution to log_{10}(48)+log_{10}(75) is 2log_{10}(60)

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simplify log_{10}(48)+log_{10}(75)

simplify

lo g_{10} (48) + lo g_{10} (75)

2 lo g_{10} (60)

Decimal Notation

3.55630 \dots

Solution steps

lo g_{10} (48) + lo g_{10} (75)

Apply log rule:

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

lo g_{10} (48) + lo g_{10} (75) = lo g_{10} (48 \cdot 75)

= lo g_{10} (48 \cdot 75)

Multiply the numbers:

48 \cdot 75 = 3600

= lo g_{10} (3600)

Factor the number:

3600 = 6 0^{2}

= lo g_{10} (6 0^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (6 0^{2}) = 2 lo g_{10} (60)

= 2 lo g_{10} (60)

\frac{3}{2} ln (2)

lo g_{2} (x^{2} - 4) - lo g_{2} (x + 2)

2 lo g_{10} (3) + lo g_{10} (2)

3 ln (x) - 6 ln (y)

\frac{1}{5} ln (x) + ln (y)

What is log_{10}(48)+log_{10}(75) ?
The solution to log_{10}(48)+log_{10}(75) is 2log_{10}(60)