How do you solve $10(1+0.25)^x=200$ ?

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Answer 1 · 2018-07-17T12:06:06

$x~~13.425$

$10(1+0.25)^x=200$

Let's divide by 10 on both sides and simplify within the brackets:

$1.25^x=20$

Take the log on both sides:

$log(1.25^x)=log20$

$xlog1.25=log20$

$x=log20/log1.25~~13.425$

Let's check it:

$10(1+0.25)^13.425=199.994$

Had we rounded with more significant digits, we would have gotten even closer to 200.

How do you solve 10(1+0.25)^x=20010(1+0.25)^x=200?