What is 3ln(2)+ln(x-2)-2ln(7) ?

The solution to 3ln(2)+ln(x-2)-2ln(7) is ln((8(x-2))/(49))

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simplify 3ln(2)+ln(x-2)-2ln(7)

simplify

3 ln (2) + ln (x - 2) - 2 ln (7)

ln (\frac{8 ( x - 2 )}{49})

Solution steps

3 ln (2) + ln (x - 2) - 2 ln (7)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) + ln (x - 2) - 2 ln (7)

Apply log rule:

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

ln (2^{3}) + ln (x - 2) = ln (2^{3} (x - 2))

= ln (2^{3} (x - 2)) - 2 ln (7)

2^{3} = 8

= ln (8 (x - 2)) - 2 ln (7)

Apply log rule:

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

2 ln (7) = ln (7^{2})

= ln (8 (x - 2)) - ln (7^{2})

Apply log rule:

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

ln (8 (x - 2)) - ln (7^{2}) = ln (\frac{8 ( x - 2 )}{7 ^{2}})

= ln (\frac{8 ( x - 2 )}{7 ^{2}})

7^{2} = 49

= ln (\frac{8 ( x - 2 )}{49})

lo g_{2} (\frac{4}{x + 3})

lo g_{10} (\frac{x ^{2}}{y ^{5}})

(lo g_{c} (x) - lo g_{c} (y)) + 7 lo g_{c} (v)

10 lo g_{6} (x) - 2 lo g_{6} (y)

lo g_{10} (23 pq)

What is 3ln(2)+ln(x-2)-2ln(7) ?
The solution to 3ln(2)+ln(x-2)-2ln(7) is ln((8(x-2))/(49))