What is ln((e^xln(3))/3) ?

The solution to ln((e^xln(3))/3) is x+ln(ln(3))-ln(3)

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simplify ln((e^xln(3))/3)

simplify

ln (\frac{e ^{x} ln ( 3 )}{3})

x + ln (ln (3)) - ln (3)

Solution steps

ln (\frac{e ^{x} ln ( 3 )}{3})

Apply log rule:

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

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

= ln (ln (3) e^{x}) - ln (3)

Apply log rule:

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

ln (e^{x} ln (3)) = ln (e^{x}) + ln (ln (3))

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

Apply log rule:

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

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

= x ln (e) + ln (ln (3)) - ln (3)

x ln (e) = x

= x + ln (ln (3)) - ln (3)

- lo g_{10} (7.5 \cdot 1 0^{- 3})

- lo g_{10} (4.3 \cdot 1 0^{- 7})

- \frac{5}{6} lo g_{2} (\frac{5}{6}) - \frac{1}{6} lo g_{2} (\frac{1}{6})

lo g_{10} (100000 x)

lo g_{9} (\frac{x ^{5}}{9})

What is ln((e^xln(3))/3) ?
The solution to ln((e^xln(3))/3) is x+ln(ln(3))-ln(3)