What is simplify-log_{10}(1.8*10^{-5})-log_{10}(0.465) ?

The solution to simplify-log_{10}(1.8*10^{-5})-log_{10}(0.465) is -log_{10}(837)+8

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simplify-log_{10}(1.8*10^{-5})-log_{10}(0.465)

simplify

- lo g_{10} (1.8 \cdot 1 0^{- 5}) - lo g_{10} (0.465)

- lo g_{10} (837) + 8

Decimal Notation

5.07727 \dots

Solution steps

- lo g_{10} (1.8 \cdot 1 0^{- 5}) - lo g_{10} (0.465)

Apply log rule:

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

- lo g_{10} (0.465) - lo g_{10} (1.8 \cdot 1 0^{- 5}) = lo g_{10} (0.465 \cdot 1.8 \cdot 1 0^{- 5})

= - lo g_{10} (0.465 \cdot 1.8 \cdot 1 0^{- 5})

Simplify

0.465 \cdot 1.8 \cdot 1 0^{- 5} : 0.00000837

= - lo g_{10} (0.00000837)

0.00000837 = \frac{837}{100000000}

= - lo g_{10} (\frac{837}{100000000})

Simplify

lo g_{10} (\frac{837}{100000000}) : lo g_{10} (837) - 8

= - (lo g_{10} (837) - 8)

Distribute parentheses

= - (lo g_{10} (837)) - (- 8)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (837) + 8

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lo g_{8} (64 x^{2})

5 lo g_{2} (5) + 5 lo g_{2} (7) - 15 lo g_{2} (6)

What is simplify-log_{10}(1.8*10^{-5})-log_{10}(0.465) ?
The solution to simplify-log_{10}(1.8*10^{-5})-log_{10}(0.465) is -log_{10}(837)+8