What is simplify-log_{10}(1.541*10^{-5}) ?

The solution to simplify-log_{10}(1.541*10^{-5}) is -log_{10}(1.541)+5

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simplify-log_{10}(1.541*10^{-5})

simplify

- lo g_{10} (1.541 \cdot 1 0^{- 5})

- lo g_{10} (1.541) + 5

Decimal Notation

4.81219 \dots

Solution steps

- lo g_{10} (1.541 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (1.541 \cdot 1 0^{- 5}) = lo g_{10} (1.541) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (1.541) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (1.541) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (1.541) - 5)

Distribute parentheses

= - (lo g_{10} (1.541)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (1.541) + 5

\frac{1}{3} ln (100) + \frac{2}{3} ln (200)

- ln (x) + 2 ln (x + 1) + 2 ln (x - 1)

ln (50 x)

ln (n^{2} + k^{2}) - ln (n^{2})

2 ln (2) + 2 β + 2 ln (x) + 3 e^{β} x

What is simplify-log_{10}(1.541*10^{-5}) ?
The solution to simplify-log_{10}(1.541*10^{-5}) is -log_{10}(1.541)+5