What is ln((1.1*10^6)/(1.2*10^3)) ?

The solution to ln((1.1*10^6)/(1.2*10^3)) is 3ln(10)+ln(1.1)-ln(1.2)

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Popular >

simplify ln((1.110^6)/(1.210^3))

simplify

ln (\frac{1.1 \cdot 1 0 ^{6}}{1.2 \cdot 1 0 ^{3}})

3 ln (10) + ln (1.1) - ln (1.2)

Decimal Notation

6.82074 \dots

Solution steps

ln (\frac{1.1 \cdot 1 0 ^{6}}{1.2 \cdot 1 0 ^{3}})

Apply log rule:

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

ln (\frac{1.1 \cdot 1 0 ^{6}}{1.2 \cdot 1 0 ^{3}}) = ln (1.1 \cdot 1 0^{6}) - ln (1.2 \cdot 1 0^{3})

= ln (1 0^{6} \cdot 1.1) - ln (1 0^{3} \cdot 1.2)

Apply log rule:

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

ln (1.1 \cdot 1 0^{6}) = ln (1.1) + ln (1 0^{6}), ln (1.2 \cdot 1 0^{3}) = ln (1.2) + ln (1 0^{3})

= ln (1.1) + ln (1 0^{6}) - (ln (1.2) + ln (1 0^{3}))

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= ln (1.1) + 6 ln (10) - (ln (1.2) + ln (1 0^{3}))

Apply log rule:

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

ln (1 0^{3}) = 3 ln (10)

= ln (1.1) + 6 ln (10) - (ln (1.2) + 3 ln (10))

- (ln (1.2) + 3 ln (10)) : - ln (1.2) - 3 ln (10)

= ln (1.1) + 6 ln (10) - ln (1.2) - 3 ln (10)

Simplify

ln (1.1) + 6 ln (10) - ln (1.2) - 3 ln (10) : 3 ln (10) + ln (1.1) - ln (1.2)

= 3 ln (10) + ln (1.1) - ln (1.2)

- lo g_{10} (1.46 \cdot 1 0^{- 9})

ln (4 y)

\frac{1}{2} ln ∣ sec (x) ∣

ln (x^{2} (x - 1) (x^{2} + 4)^{3})

ln (17 x^{- 3} y)

What is ln((1.1*10^6)/(1.2*10^3)) ?
The solution to ln((1.1*10^6)/(1.2*10^3)) is 3ln(10)+ln(1.1)-ln(1.2)