a) substitution (refer to statements 1 and 2)
b) definition of supplementary
c) subtraction property of equality
Let garret’s age be x
x + 2 + (x + 3) + 2 = 39
2x + 7 = 39
2x = 32
x = 32/2
x = 16
Garrett’s age after two years = 16 + 2 = 18
Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
<u>9x</u> = <u>3y + 5</u>
9 9
x = 1/3y + 5/9
x - 5/9 = 1/3y + 5/9 - 5/9
x - 5/9 = 1/3y
3(x - 5/9) = 1/3y · 3
3x - 1 2/3 = y
y = 3x - 1 2/3
A. but I would double check on that one first.
