What is log_{5}(45)-log_{5}(3) ?

The solution to log_{5}(45)-log_{5}(3) is log_{5}(15)

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simplify log_{5}(45)-log_{5}(3)

simplify

lo g_{5} (45) - lo g_{5} (3)

lo g_{5} (15)

Decimal Notation

1.68260 \dots

Solution steps

lo g_{5} (45) - lo g_{5} (3)

Apply log rule:

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

lo g_{5} (45) - lo g_{5} (3) = lo g_{5} (\frac{45}{3})

= lo g_{5} (\frac{45}{3})

Divide the numbers:

\frac{45}{3} = 15

= lo g_{5} (15)

\frac{15 ln ( 7 ) - 6 ln ( 2 )}{2 ln ( 28 )}

3 ln (5) + \frac{1}{2} ln (9) - 3 ln (3) - 5 ln (25)

- (\frac{6}{8}) lo g_{2} (\frac{6}{8}) - (\frac{2}{8}) lo g_{2} (\frac{2}{8})

lo g_{10} (a) + 2 lo g_{10} (c)

ln (2 sinh (\frac{h w}{2 k x}))

What is log_{5}(45)-log_{5}(3) ?
The solution to log_{5}(45)-log_{5}(3) is log_{5}(15)