What is simplify-log_{10}(6.46*10^{-5}) ?

The solution to simplify-log_{10}(6.46*10^{-5}) is -log_{10}(6.46)+5

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simplify-log_{10}(6.46*10^{-5})

simplify

- lo g_{10} (6.46 \cdot 1 0^{- 5})

- lo g_{10} (6.46) + 5

Decimal Notation

4.18976 \dots

Solution steps

- lo g_{10} (6.46 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (6.46 \cdot 1 0^{- 5}) = lo g_{10} (6.46) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (6.46) + 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} (6.46) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (6.46) - 5)

Distribute parentheses

= - (lo g_{10} (6.46)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (6.46) + 5

3 lo g_{10} (2) - lo g_{10} (4) + 2 lo g_{10} (5)

lo g_{e} (\frac{a + x}{x})

\frac{ln ( 1500 ) - ln ( 1500 - 19200 )}{ln ( 1.03 )}

1.5 ln (\frac{13}{9})

2.1 \cdot ln (\frac{273}{233})

What is simplify-log_{10}(6.46*10^{-5}) ?
The solution to simplify-log_{10}(6.46*10^{-5}) is -log_{10}(6.46)+5