What is 5ln(2)-ln(x)-ln(17) ?

The solution to 5ln(2)-ln(x)-ln(17) is ln((32)/(17x))

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simplify 5ln(2)-ln(x)-ln(17)

simplify

5 ln (2) - ln (x) - ln (17)

ln (\frac{32}{17 x})

Solution steps

5 ln (2) - ln (x) - ln (17)

Apply log rule:

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

5 ln (2) = ln (2^{5})

= ln (2^{5}) - ln (x) - ln (17)

Apply log rule:

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

ln (2^{5}) - ln (x) = ln (\frac{2 ^{5}}{x})

= ln (\frac{2 ^{5}}{x}) - ln (17)

2^{5} = 32

= ln (\frac{32}{x}) - ln (17)

Apply log rule:

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

ln (\frac{32}{x}) - ln (17) = ln (\frac{\frac{32}{x}}{17})

= ln (\frac{\frac{32}{x}}{17})

Apply the fraction rule:

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

= ln (\frac{32}{17 x})

ln (3) + ln (\frac{31}{8})

10 lo g_{10} (\frac{( 159 \cdot 1 0 ^{- 9} )}{20 \cdot 1 0 ^{- 3}})

0.5 ln (\frac{3}{4}) + 3 ln (1.5)

(\frac{3 ln ^{2} ( 3 x ) + 1}{x ( ln ^{3} ( 3 x ) + ln ( x ) )}) ln (x)

- 2 \cdot lo g_{10} (0.35) - lo g_{10} (0.17)

What is 5ln(2)-ln(x)-ln(17) ?
The solution to 5ln(2)-ln(x)-ln(17) is ln((32)/(17x))