What is 15ln|(15)^2+7|-15ln|(0)^2+7| ?

The solution to 15ln|(15)^2+7|-15ln|(0)^2+7| is 15ln(232/7)

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simplify 15ln|(15)^2+7|-15ln|(0)^2+7|

simplify

15 ln (15)^{2} + 7 - 15 ln (0)^{2} + 7

15 ln (\frac{232}{7})

Decimal Notation

52.51240 \dots

Solution steps

15 ln (15)^{2} + 7 - 15 ln (0)^{2} + 7

Apply log rule:

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

15 ln 1 5^{2} + 7 = ln (1 5^{2} + 7^{15})

= ln (1 5^{2} + 7^{15}) - 15 ln 0^{2} + 7

Apply log rule:

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

15 ln 0^{2} + 7 = ln (0^{2} + 7^{15})

= ln (1 5^{2} + 7^{15}) - ln (0^{2} + 7^{15})

Apply log rule:

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

ln (1 5^{2} + 7^{15}) - ln (0^{2} + 7^{15}) = ln (\frac{1 5 ^{2} + 7 ^{15}}{∣ 0 ^{2} + 7 ∣ ^{15}})

= ln (\frac{1 5 ^{2} + 7 ^{15}}{∣ 0 ^{2} + 7 ∣ ^{15}})

\frac{1 5 ^{2} + 7 ^{15}}{∣ 0 ^{2} + 7 ∣ ^{15}} = \frac{23 2 ^{15}}{7 ^{15}}

= ln (\frac{23 2 ^{15}}{7 ^{15}})

Combine same powers :

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

= ln ((\frac{232}{7})^{15})

Apply log rule

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

assuming

x \geq 0

= 15 ln (\frac{232}{7})

4 ln (c) (ln (a) - 3 ln (b))

\frac{1}{2} ln (x) + \frac{1}{2} ln (\frac{p x}{p y} x)

ln (\frac{20}{8})

ln (\frac{1}{\frac{95}{100}})

ln (\frac{1}{w})

What is 15ln|(15)^2+7|-15ln|(0)^2+7| ?
The solution to 15ln|(15)^2+7|-15ln|(0)^2+7| is 15ln(232/7)