Asked by Caleb
Ed borrowed 1,500 for 4 months at 13.5 %. How much did he have to pay back under an add-on plan?
Answers
Answered by
Steve
^ and log are inverse operations
x+8 - 8 = x
x/8 * 8 = x
(√x)^2 = x
log<sub>8</sub>8<sup>x</sup> = x
8<sup>log<sub>8</sub>x</sup> = x
The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier.
The definition of log<sub>8</sub>x is that power of 8 which we need to get x.
Now, 9^x = 57 is a bit trickier. Recall that
log<sub>9</sub>N is the power of 9 you need to get N. So,
log<sub>9</sub>57 is the power of 9 you need to get 57.
Taking log<sub>9</sub> of both sides gives you
log<sub>9</sub>9<sup>x</sup> = log<sub>9</sub>57
But since log<sub>9</sub>9<sup>x</sup> = x, you end up with
x = log<sub>9</sub>57
x+8 - 8 = x
x/8 * 8 = x
(√x)^2 = x
log<sub>8</sub>8<sup>x</sup> = x
8<sup>log<sub>8</sub>x</sup> = x
The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier.
The definition of log<sub>8</sub>x is that power of 8 which we need to get x.
Now, 9^x = 57 is a bit trickier. Recall that
log<sub>9</sub>N is the power of 9 you need to get N. So,
log<sub>9</sub>57 is the power of 9 you need to get 57.
Taking log<sub>9</sub> of both sides gives you
log<sub>9</sub>9<sup>x</sup> = log<sub>9</sub>57
But since log<sub>9</sub>9<sup>x</sup> = x, you end up with
x = log<sub>9</sub>57
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