What is simplify-log_{10}(1.35(10^{-10})) ?

The solution to simplify-log_{10}(1.35(10^{-10})) is -log_{10}(1.35)+10

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simplify-log_{10}(1.35(10^{-10}))

simplify

- lo g_{10} (1.35 (1 0^{- 10}))

- lo g_{10} (1.35) + 10

Decimal Notation

9.86966 \dots

Solution steps

- lo g_{10} (1.35 (1 0^{- 10}))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (1.35 (1 0^{- 10})) = lo g_{10} (1.35) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (1.35) + lo g_{10} (1 0^{- 10}))

Apply log rule:

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

lo g_{10} (1 0^{- 10}) = - 10 lo g_{10} (10)

= - (lo g_{10} (1.35) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (1.35) - 10)

Distribute parentheses

= - (lo g_{10} (1.35)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (1.35) + 10

ln (1) + ln (3) - 2 ln (2)

ln (\frac{0.27}{2.21 \cdot 1 0 ^{4}}) \cdot \frac{8.314}{90315}

0.7 + 0.1 \cdot lo g_{10} (\frac{( 2.15 )}{15})

2 lo g_{8} (x) - \frac{1}{2} lo g_{8} (w) + 7 lo g_{8} (z)

ln (32) + ln (8)

What is simplify-log_{10}(1.35(10^{-10})) ?
The solution to simplify-log_{10}(1.35(10^{-10})) is -log_{10}(1.35)+10