What is log_{4}(5)+log_{4}(12)-log_{4}(3.75) ?

The solution to log_{4}(5)+log_{4}(12)-log_{4}(3.75) is 2

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simplify log_{4}(5)+log_{4}(12)-log_{4}(3.75)

simplify

lo g_{4} (5) + lo g_{4} (12) - lo g_{4} (3.75)

2

Solution steps

lo g_{4} (5) + lo g_{4} (12) - lo g_{4} (3.75)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{4} (5) + lo g_{4} (12) = lo g_{4} (5 \cdot 12)

= lo g_{4} (5 \cdot 12) - lo g_{4} (3.75)

Multiply the numbers:

5 \cdot 12 = 60

= lo g_{4} (60) - lo g_{4} (3.75)

Apply log rule:

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

lo g_{4} (60) - lo g_{4} (3.75) = lo g_{4} (\frac{60}{3.75})

= lo g_{4} (\frac{60}{3.75})

Divide the numbers:

\frac{60}{3.75} = 16

= lo g_{4} (16)

Rewrite

16

in power-base form:

16 = 4^{2}

= lo g_{4} (4^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} (4^{2}) = 2 lo g_{4} (4)

= 2 lo g_{4} (4)

Apply log rule:

lo g_{a} (a) = 1

lo g_{4} (4) = 1

= 2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 2

lo g_{7} (49 x^{5})

lo g_{\frac{1}{2}} (\frac{2}{3})

lo g_{2} (\frac{y}{8})

ln (\frac{π ^{7}}{8})

lo g_{10} (x + 5) + 2 lo g_{10} (x)

What is log_{4}(5)+log_{4}(12)-log_{4}(3.75) ?
The solution to log_{4}(5)+log_{4}(12)-log_{4}(3.75) is 2