What is ln(25)-2ln(125)+ln(5^4)+6ln(5) ?

The solution to ln(25)-2ln(125)+ln(5^4)+6ln(5) is 6ln(5)

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simplify ln(25)-2ln(125)+ln(5^4)+6ln(5)

simplify

ln (25) - 2 ln (125) + ln (5^{4}) + 6 ln (5)

6 ln (5)

Decimal Notation

9.65662 \dots

Solution steps

ln (25) - 2 ln (125) + ln (5^{4}) + 6 ln (5)

Apply log rule:

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

2 ln (125) = ln (12 5^{2})

= ln (25) - ln (12 5^{2}) + ln (5^{4}) + 6 ln (5)

Apply log rule:

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

ln (25) - ln (12 5^{2}) = ln (\frac{25}{12 5 ^{2}})

= ln (\frac{25}{12 5 ^{2}}) + ln (5^{4}) + 6 ln (5)

\frac{25}{12 5 ^{2}} = \frac{1}{625}

= ln (\frac{1}{625}) + ln (5^{4}) + 6 ln (5)

Apply log rule

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

assuming

x \geq 0

= ln (\frac{1}{625}) + 4 ln (5) + 6 ln (5)

Add similar elements:

4 ln (5) + 6 ln (5) = 10 ln (5)

= ln (\frac{1}{625}) + 10 ln (5)

ln (\frac{1}{625}) = - 4 ln (5)

= - 4 ln (5) + 10 ln (5)

Add similar elements:

- 4 ln (5) + 10 ln (5) = 6 ln (5)

= 6 ln (5)

ln (18) - ln (2)

ln (c e^{- c})

lo g_{2} ((2 y - 4)^{3})

ln (t^{2} x y)

ln (x) - 2 ln (z) - \frac{1}{6} ln (y)

What is ln(25)-2ln(125)+ln(5^4)+6ln(5) ?
The solution to ln(25)-2ln(125)+ln(5^4)+6ln(5) is 6ln(5)