What is simplify-50ln(300)+50ln(450) ?

The solution to simplify-50ln(300)+50ln(450) is 50ln(3/2)

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simplify-50ln(300)+50ln(450)

simplify

- 50 ln (300) + 50 ln (450)

50 ln (\frac{3}{2})

Decimal Notation

20.27325 \dots

Solution steps

- 50 ln (300) + 50 ln (450)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

50 ln (300) = ln (30 0^{50})

= - ln (30 0^{50}) + 50 ln (450)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

50 ln (450) = ln (45 0^{50})

= - ln (30 0^{50}) + ln (45 0^{50})

Apply log rule:

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

ln (45 0^{50}) - ln (30 0^{50}) = ln (\frac{45 0 ^{50}}{30 0 ^{50}})

= ln (\frac{45 0 ^{50}}{30 0 ^{50}})

\frac{45 0 ^{50}}{30 0 ^{50}} = \frac{3 ^{50}}{2 ^{50}}

= ln (\frac{3 ^{50}}{2 ^{50}})

Combine same powers :

\frac{x ^{n}}{y ^{n}} = (\frac{x}{y})^{n}

= ln ((\frac{3}{2})^{50})

Apply log rule

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

assuming

x \geq 0

= 50 ln (\frac{3}{2})

\frac{ln ( x )}{ln ( y ) - ln ( x )}

- ln (\frac{0.5}{ln ( 2 )})

ln (\frac{9}{6})

- lo g_{10} (2.49 \cdot 1 0^{- 7})

lo g_{e} (8000) - lo g_{e} (4000)

What is simplify-50ln(300)+50ln(450) ?
The solution to simplify-50ln(300)+50ln(450) is 50ln(3/2)