Question

If log 2 = x and log 3 = y, write each logarithm in terms of x and y.

Answer 1

Answer:

• a) x+y
• b) 2x+y
• c) -x
• d) x+y+1
• e) y-x
• f) x/2

Step-by-step explanation:

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

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$\text{a) }\log{6}=\log{(2\cdot 3)}=\log{2}+\log{{3}=\boxed{x+y}$

$\text{b) }\log{12}=\log{(2^23)}=2\log{2}+\log{3}=\boxed{2x+y}$

$\text{c) }\log{(1/2)}=\log{2^{-1}}=-\log{2}=\boxed{-x}$

$\text{d) }\log{60}=\log{(2\cdot 3\cdot 10)}=\log{2}+\log{3}+\log{10}=\boxed{x+y+1}$

$\text{e) }\log{1.5}=\log{3\cdot2^{-1}}=\log{3}-\log{2}=\boxed{y-x}$

$\text{f) }\log{\sqrt{2}}=\log{2^{\frac{1}{2}}}=\dfrac{1}{2}\log{2}=\boxed{\dfrac{x}{2}}$