What is join (2ln(55/9))/(ln(2)) ?

The solution to join (2ln(55/9))/(ln(2)) is (ln(3025/81))/(ln(2))

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join (2ln(55/9))/(ln(2))

join

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )}

\frac{ln ( \frac{3025}{81} )}{ln ( 2 )}

Decimal Notation

5.22286 \dots

Solution steps

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )}

Apply log rule:

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

2 ln (\frac{55}{9}) = ln ((\frac{55}{9})^{2})

= \frac{ln ( ( \frac{55}{9} ) ^{2} )}{ln ( 2 )}

(\frac{55}{9})^{2} = \frac{5 5 ^{2}}{9 ^{2}}

= \frac{ln ( \frac{5 5 ^{2}}{9 ^{2}} )}{ln ( 2 )}

\frac{5 5 ^{2}}{9 ^{2}} = \frac{3025}{81}

= \frac{ln ( \frac{3025}{81} )}{ln ( 2 )}

lo g_{10} (\frac{x z ^{2}}{y})

ln (x + 3) - ln (4)

2 ln (10) - ln (5) - 2 ln (2) + ln (3)

- lo g_{10} (8.41 \cdot 0.001)

ln (\frac{0.5}{1.5})

What is join (2ln(55/9))/(ln(2)) ?
The solution to join (2ln(55/9))/(ln(2)) is (ln(3025/81))/(ln(2))