Michael B. answered • 02/21/13

Seasoned and experienced tutor with extensive science background

remember some of the properties of logarithms and exponents:

**log _{a}(x) = b** means that

**a**

^{b}**= x**

**log _{a}(y) = c** means that

**a**

^{c}= y**log _{a}(xy)** =

**log**

_{a}**(x) + log**

_{a}**(y)**

**= b + c**

**log _{a}(x/y) = log_{a}(x) - log_{a}(y) = b - c**

using a numerical example with a = 2, x = 4, and y = 8

log_{2} (4*8) = log_{2}(4) + log_{2}(8) = 2 + 3 = 5

you can check that since 2^{5} = 32 = 8*4

again using the same numbers for a, x, and y but this time dividing

log_{2}(4/8) = log_{2}(4) - log_{2}(8) = 2 - 3 = -1

since 2^{-1} = 1/2 = 4/8

Now, you just combine the two steps

this time I'll add an "m" value for you but will leave the writing of the general equation to you:

for a = 2, x = 4, y = 8, m = 32

log_{2}[(4*8)/32] = log_{2}(4) + log_{2}(8) - log_{2}32 = 2 + 3 - 5 = 0

2^{0} = (32/32) = 1