What is log_{10}(810)+log_{10}(0.03) ?

The solution to log_{10}(810)+log_{10}(0.03) is 5log_{10}(3)-1

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simplify log_{10}(810)+log_{10}(0.03)

simplify

lo g_{10} (810) + lo g_{10} (0.03)

5 lo g_{10} (3) - 1

Decimal Notation

1.38560 \dots

Solution steps

lo g_{10} (810) + lo g_{10} (0.03)

Apply log rule:

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

lo g_{10} (810) + lo g_{10} (0.03) = lo g_{10} (810 \cdot 0.03)

= lo g_{10} (810 \cdot 0.03)

Multiply the numbers:

810 \cdot 0.03 = 24.3

= lo g_{10} (24.3)

24.3 = \frac{243}{10}

= lo g_{10} (\frac{243}{10})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{243}{10}) = lo g_{10} (243) - lo g_{10} (10)

= lo g_{10} (243) - lo g_{10} (10)

Simplify

lo g_{10} (10) : 1

Rewrite

243

in power-base form:

243 = 3^{5}

= lo g_{10} (3^{5}) - 1

Apply log rule:

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

lo g_{10} (3^{5}) = 5 lo g_{10} (3)

= 5 lo g_{10} (3) - 1

- \frac{1}{3} (ln (26) - ln (5))

ln (\frac{1}{t})

ln ∣ 4 ∣ - ln (x)

lo g_{e} (\frac{1}{12})

ln ((x + 2)^{3} (x + 7))

What is log_{10}(810)+log_{10}(0.03) ?
The solution to log_{10}(810)+log_{10}(0.03) is 5log_{10}(3)-1