What is ln(x-3)-ln(x-7)+10ln(x) ?

The solution to ln(x-3)-ln(x-7)+10ln(x) is ln((x^{10}(x-3))/(x-7))

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simplify ln(x-3)-ln(x-7)+10ln(x)

simplify

ln (x - 3) - ln (x - 7) + 10 ln (x)

ln (\frac{x ^{10} ( x - 3 )}{x - 7})

Solution steps

ln (x - 3) - ln (x - 7) + 10 ln (x)

Apply log rule:

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

ln (x - 3) - ln (x - 7) = ln (\frac{x - 3}{x - 7})

= ln (\frac{x - 3}{x - 7}) + 10 ln (x)

Apply log rule:

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

10 ln (x) = ln (x^{10})

= ln (\frac{x - 3}{x - 7}) + ln (x^{10})

Apply log rule:

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

ln (\frac{x - 3}{x - 7}) + ln (x^{10}) = ln (\frac{x - 3}{x - 7} x^{10})

= ln (\frac{x - 3}{x - 7} x^{10})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{x ^{10} ( x - 3 )}{x - 7})

ln (4 \cdot 2)

ln (\frac{1000000}{465663})

- ln (\frac{5}{a ^{- 2}})

ln (2 m x^{m - 1})

ln (x + 1) 2 + ln (y + 1) 3

What is ln(x-3)-ln(x-7)+10ln(x) ?
The solution to ln(x-3)-ln(x-7)+10ln(x) is ln((x^{10}(x-3))/(x-7))