How do you solve $5000(1.09^(12x)) = 9500$ ?

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Answer 1 · 2016-01-07T00:21:07

$x=0.62066899187$

Divide both sides by $5000$ .

$1.09^(12x)=1.9$

To get the $x$ out of the exponent, or to undo the exponential function, take the logarithm with base $1.09$ of both sides.

$log_1.09(1.09^(12x))=log_1.09 1.9$

$12x=log_1.09 1.9$

Divide both sides by $12$ .

$x=(log_1.09 1.9)/12$

To find the value of this in a calculator, use the change of base formula, which states that

$log_ab=log_cb/log_ca$

Thus

$log_1.09 1.9=ln1.9/ln1.09$

so

$x=(ln1.9/ln1.09)(1/12)=ln1.9/(12ln1.09)=0.62066899187$

How do you solve 5000(1.09^(12x)) = 95005000(1.09^(12x)) = 9500?