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
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
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).
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).