What is expand log_{e}(((a^m*b^n))/c) ?

The solution to expand log_{e}(((a^m*b^n))/c) is mln(a)+nln(b)-ln(c)

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expand log_{e}(((a^m*b^n))/c)

expand

lo g_{e} (\frac{( a ^{m} \cdot b ^{n} )}{c})

m ln (a) + n ln (b) - ln (c)

Solution steps

lo g_{e} (\frac{( a ^{m} b ^{n} )}{c})

Apply log rule:

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

lo g_{e} (\frac{( a ^{m} b ^{n} )}{c}) = lo g_{e} ((a^{m} b^{n})) - lo g_{e} (c)

= lo g_{e} (a^{m} b^{n}) - lo g_{e} (c)

Apply log rule:

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

lo g_{e} (a^{m} b^{n}) = lo g_{e} (a^{m}) + lo g_{e} (b^{n})

= lo g_{e} (a^{m}) + lo g_{e} (b^{n}) - lo g_{e} (c)

Apply log rule:

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

lo g_{e} (a^{m}) = m lo g_{e} (a)

= m lo g_{e} (a) + lo g_{e} (b^{n}) - lo g_{e} (c)

Apply log rule:

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

lo g_{e} (b^{n}) = n lo g_{e} (b)

= m lo g_{e} (a) + n lo g_{e} (b) - lo g_{e} (c)

Simplify

lo g_{e} (a) : ln (a)

= m ln (a) + n lo g_{e} (b) - lo g_{e} (c)

Simplify

lo g_{e} (b) : ln (b)

= m ln (a) + n ln (b) - lo g_{e} (c)

Apply log rule:

lo g_{e} (x) = ln (x)

= m ln (a) + n ln (b) - ln (c)

ln (\frac{x + y}{2}) \cdot 2

(ln (90) - ln (95)) \cdot 100

0.026 ln (0.135 \cdot 1 0^{16})

ln (\frac{x ^{4} y}{z ^{6}})

2 ln (6) - 3 ln (8)

What is expand log_{e}(((a^m*b^n))/c) ?
The solution to expand log_{e}(((a^m*b^n))/c) is mln(a)+nln(b)-ln(c)