What is log_{10}(8)+log_{10}(4) ?

The solution to log_{10}(8)+log_{10}(4) is 5log_{10}(2)

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simplify log_{10}(8)+log_{10}(4)

simplify

lo g_{10} (8) + lo g_{10} (4)

5 lo g_{10} (2)

Decimal Notation

1.50514 \dots

Solution steps

lo g_{10} (8) + lo g_{10} (4)

Apply log rule:

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

lo g_{10} (8) + lo g_{10} (4) = lo g_{10} (8 \cdot 4)

= lo g_{10} (8 \cdot 4)

Multiply the numbers:

8 \cdot 4 = 32

= lo g_{10} (32)

Factor the number:

32 = 2^{5}

= lo g_{10} (2^{5})

Apply log rule:

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

lo g_{10} (2^{5}) = 5 lo g_{10} (2)

= 5 lo g_{10} (2)

lo g_{4} (\frac{12}{x})

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

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

6 [ln (z) + ln (z + 7)] - 3 ln (z - 7)

ln (x \frac{y}{2})

What is log_{10}(8)+log_{10}(4) ?
The solution to log_{10}(8)+log_{10}(4) is 5log_{10}(2)