What is (ln(3)+4-4ln(10))/(ln(10)+1) ?

The solution to (ln(3)+4-4ln(10))/(ln(10)+1) is (ln(3/10000)+4)/(ln(10)+1)

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simplify (ln(3)+4-4ln(10))/(ln(10)+1)

simplify

\frac{ln ( 3 ) + 4 - 4 ln ( 10 )}{ln ( 10 ) + 1}

\frac{ln ( \frac{3}{10000} ) + 4}{ln ( 10 ) + 1}

Decimal Notation

- 1.24500 \dots

Solution steps

\frac{ln ( 3 ) + 4 - 4 ln ( 10 )}{ln ( 10 ) + 1}

Apply log rule:

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

4 ln (10) = ln (1 0^{4})

= \frac{ln ( 3 ) + 4 - ln ( 1 0 ^{4} )}{ln ( 10 ) + 1}

Apply log rule:

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

ln (3) - ln (1 0^{4}) = ln (\frac{3}{1 0 ^{4}})

= \frac{ln ( \frac{3}{1 0 ^{4}} ) + 4}{ln ( 10 ) + 1}

1 0^{4} = 10000

= \frac{ln ( \frac{3}{10000} ) + 4}{ln ( 10 ) + 1}

ln (k + 1) - ln (k)

- lo g_{10} (x) + lo g_{10} (0.9091 x + 0.001818)

- lo g_{10} (5.45 \cdot 1 0^{3})

ln \frac{( x ^{\frac{1}{3}} )}{x ^{6} 1 + x ^{2}}

What is (ln(3)+4-4ln(10))/(ln(10)+1) ?
The solution to (ln(3)+4-4ln(10))/(ln(10)+1) is (ln(3/10000)+4)/(ln(10)+1)