What is simplify-log_{10}(1/40000) ?

The solution to simplify-log_{10}(1/40000) is 2log_{10}(200)

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simplify-log_{10}(1/40000)

simplify

- lo g_{10} (\frac{1}{40000})

2 lo g_{10} (200)

Decimal Notation

4.60205 \dots

Solution steps

- lo g_{10} (\frac{1}{40000})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{1}{40000}) = lo g_{10} (1) - lo g_{10} (40000)

= - (lo g_{10} (1) - lo g_{10} (40000))

Apply log rule:

lo g_{a} (1) = 0

= - (- lo g_{10} (40000) + 0)

0 - lo g_{10} (40000) = - lo g_{10} (40000)

= - (- lo g_{10} (40000))

Apply rule

- (- a) = a

= lo g_{10} (40000)

Rewrite

40000

in power-base form:

40000 = 20 0^{2}

= lo g_{10} (20 0^{2})

Apply log rule:

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

lo g_{10} (20 0^{2}) = 2 lo g_{10} (200)

= 2 lo g_{10} (200)

ln (\frac{x ^{2}}{5})

\frac{0.125 \cdot 16}{63.617 \cdot 720} \cdot ln (\frac{130}{70})

(75.3) ln (\frac{373}{300})

x^{2} + ln (2 x)

ln (a e^{- \frac{b}{c}})

What is simplify-log_{10}(1/40000) ?
The solution to simplify-log_{10}(1/40000) is 2log_{10}(200)