MATH HELP-How would i solve for 'a'
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MATH HELP-How would i solve for 'a'

[From: ] [author: ] [Date: 11-09-06] [Hit: ]
03 log a = log 1.log a = (log 1.0012) / 0.log a = 0.a = 10^0.a = 1.......
a^(0.03)=1.0012

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a^(0.03) = 1.0012
log a^(0.03) = log 1.0012
0.03 log a = log 1.0012
log a = (log 1.0012) / 0.03
log a = 0.01736136
a = 10^0.01736136
a = 1.0407858

Another way to do this is to consider that (a^n)^m = a^(nm), and that a^1 = a.
a^(0.03) = 1.0012
Now raise each side to the 33.333333... power, which sets the left side to "a" alone, because:
(a^(0.03))^33.333333... = a^(0.03 * 33.333333) = a^1 = a

(a^(0.03))^33.333333 = (1.0012)^33.333333
a = 1.0407858

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.03 = 3/100

a^.03 = a^(3/100)

so....

a^3/100 = 1.0012

In order to get rid of the exponent, we have to raise both sides by the reciprocal.

(a^3/100)^100/3 = (1.0012)^100/3

a = (1.0012)^100/3

(1.0012)^100/3 is the same thing as taking the cube root of 1.0012 raised to the 100th power.

1.0012 ^100 means we just move the decimal place over 3 places to the right.

(1.0012)^100 = 1.12

Final Answer:
a = ³√1.12

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I am thinking........

a(0.03) = 1.0012.

The ^ means probably you multiply....so......

a x 0.03 = 0.03a.

Now, I am going to plug and conquer.......

0.03a = 1.0012

Then I will divide each side by 3....

0.03a/3 = 1.0012/3

The result is a = .04, because

.03 X .04 means you will have 4 decimal points (each number has 2 decimal points, so with multiplying decimals, you add the decimal points 2 + 2 = 4).
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