Question

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

a) log 6
b) log 12
c) log (1/2)
d) log 60
e) log 1.5
f) log (square root of) 2

Answer 1

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

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{√(2)}=\log{2^{(1)/(2)}}=(1)/(2)\log{2}=\boxed{(x)/(2)}`