What is join (4ln(38/45))/(ln(10)) ?

The solution to join (4ln(38/45))/(ln(10)) is (ln(2085136/4100625))/(ln(10))

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join (4ln(38/45))/(ln(10))

join

\frac{4 ln ( \frac{38}{45} )}{ln ( 10 )}

\frac{ln ( \frac{2085136}{4100625} )}{ln ( 10 )}

Decimal Notation

- 0.29371 \dots

Solution steps

\frac{4 ln ( \frac{38}{45} )}{ln ( 10 )}

Apply log rule:

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

4 ln (\frac{38}{45}) = ln ((\frac{38}{45})^{4})

= \frac{ln ( ( \frac{38}{45} ) ^{4} )}{ln ( 10 )}

(\frac{38}{45})^{4} = \frac{3 8 ^{4}}{4 5 ^{4}}

= \frac{ln ( \frac{3 8 ^{4}}{4 5 ^{4}} )}{ln ( 10 )}

\frac{3 8 ^{4}}{4 5 ^{4}} = \frac{2085136}{4100625}

= \frac{ln ( \frac{2085136}{4100625} )}{ln ( 10 )}

\frac{1}{4} lo g_{10} (945)

ln (x \cdot e^{x})

2 lo g_{10} (x) - 4 lo g_{10} (y)

- lo g_{10} (6.3 \cdot 1 0^{- 3})

lo g_{2} (12 x^{5} y^{- 2})

What is join (4ln(38/45))/(ln(10)) ?
The solution to join (4ln(38/45))/(ln(10)) is (ln(2085136/4100625))/(ln(10))