What is 50ln(10)-50ln(5)-25 ?

The solution to 50ln(10)-50ln(5)-25 is 50ln(2)-25

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simplify 50ln(10)-50ln(5)-25

simplify

50 ln (10) - 50 ln (5) - 25

50 ln (2) - 25

Decimal Notation

9.65735 \dots

Solution steps

50 ln (10) - 50 ln (5) - 25

Apply log rule:

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

50 ln (10) = ln (1 0^{50})

= ln (1 0^{50}) - 50 ln (5) - 25

Apply log rule:

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

50 ln (5) = ln (5^{50})

= ln (1 0^{50}) - ln (5^{50}) - 25

Apply log rule:

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

ln (1 0^{50}) - ln (5^{50}) = ln (\frac{1 0 ^{50}}{5 ^{50}})

= ln (\frac{1 0 ^{50}}{5 ^{50}}) - 25

\frac{1 0 ^{50}}{5 ^{50}} = 2^{50}

= ln (2^{50}) - 25

Apply log rule

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

assuming

x \geq 0

= 50 ln (2) - 25

lo g_{3} (x y^{2})

30 - 12 ln (x) - 18 ln (y)

lo g_{4} (\frac{m}{n})

ln ∣ z + 4 ∣ + 6 (\frac{1}{5} ln ∣ z - 1 ∣ - \frac{1}{5} ln ∣ z + 4 ∣)

3 ln (3 x)