What is simplify-log_{10}(1.34*10^{-11}) ?

The solution to simplify-log_{10}(1.34*10^{-11}) is -log_{10}(1.34)+11

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simplify-log_{10}(1.34*10^{-11})

simplify

- lo g_{10} (1.34 \cdot 1 0^{- 11})

- lo g_{10} (1.34) + 11

Decimal Notation

10.87289 \dots

Solution steps

- lo g_{10} (1.34 \cdot 1 0^{- 11})

Apply log rule:

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

lo g_{10} (1.34 \cdot 1 0^{- 11}) = lo g_{10} (1.34) + lo g_{10} (1 0^{- 11})

= - (lo g_{10} (1.34) + lo g_{10} (1 0^{- 11}))

Apply log rule:

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

lo g_{10} (1 0^{- 11}) = - 11 lo g_{10} (10)

= - (lo g_{10} (1.34) - 11 lo g_{10} (10))

11 lo g_{10} (10) = 11

= - (lo g_{10} (1.34) - 11)

Distribute parentheses

= - (lo g_{10} (1.34)) - (- 11)

Apply minus-plus rules

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

= - lo g_{10} (1.34) + 11

0.01 \cdot lo g_{2} (0.01) + 0.99 \cdot lo g_{2} (0.99)

ln (x^{6} (x + 9)^{7} (x^{2} + 8)^{2})

96 - 10 \cdot lo g_{10} (\frac{4 \cdot 3.14 \cdot 4 ^{2}}{2})

ln ((- 0.34)^{23.2505} (- 0.86)^{7.84805})

- lo g_{10} (1.48 \cdot 1 0^{- 3})

What is simplify-log_{10}(1.34*10^{-11}) ?
The solution to simplify-log_{10}(1.34*10^{-11}) is -log_{10}(1.34)+11