What is (log_{10}(2))/(log_{10)(5)-log_{10}(2)} ?

The solution to (log_{10}(2))/(log_{10)(5)-log_{10}(2)} is log_{5/2}(2)

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simplify (log_{10}(2))/(log_{10)(5)-log_{10}(2)}

simplify

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

lo g_{\frac{5}{2}} (2)

Decimal Notation

0.75647 \dots

Solution steps

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (5) - lo g_{10} (2) = lo g_{10} (\frac{5}{2})

= \frac{lo g _{10} ( 2 )}{lo g _{10} ( \frac{5}{2} )}

Apply log rule:

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

\frac{lo g _{10} ( 2 )}{lo g _{10} ( \frac{5}{2} )} = lo g_{\frac{5}{2}} (2)

= lo g_{\frac{5}{2}} (2)

ln (\frac{8}{10})

2 (ln (u^{3}) + ln (w^{\frac{1}{3}}) - ln (v))

lo g_{9} (x - 5) + lo g_{9} (x + 5)

ln^{2} (x) + 2 ln (x) + 2

ln (\frac{( 1 - x ^{4} ) ^{2}}{( 1 + x ^{4} ) ^{2}})

What is (log_{10}(2))/(log_{10)(5)-log_{10}(2)} ?
The solution to (log_{10}(2))/(log_{10)(5)-log_{10}(2)} is log_{5/2}(2)