What is log_{10}(0.5)+log_{10}(98) ?

The solution to log_{10}(0.5)+log_{10}(98) is 2log_{10}(7)

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simplify log_{10}(0.5)+log_{10}(98)

simplify

lo g_{10} (0.5) + lo g_{10} (98)

2 lo g_{10} (7)

Decimal Notation

1.69019 \dots

Solution steps

lo g_{10} (0.5) + lo g_{10} (98)

Apply log rule:

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

lo g_{10} (0.5) + lo g_{10} (98) = lo g_{10} (0.5 \cdot 98)

= lo g_{10} (0.5 \cdot 98)

Multiply the numbers:

0.5 \cdot 98 = 49

= lo g_{10} (49)

Factor the number:

49 = 7^{2}

= lo g_{10} (7^{2})

Apply log rule:

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

lo g_{10} (7^{2}) = 2 lo g_{10} (7)

= 2 lo g_{10} (7)

lo g_{3} (9 (x^{2} - 9))

lo g_{10} (\frac{a b ^{3}}{c ^{2}})

3 ln (\frac{1}{x})

ln (8 x^{3})

lo g_{2} (x) - lo g_{2} (x^{7})

What is log_{10}(0.5)+log_{10}(98) ?
The solution to log_{10}(0.5)+log_{10}(98) is 2log_{10}(7)