You can put this solution on YOUR website! Anytime you see an equation that has a variable in the exponent, one of the first things
you should think of is "logarithms"
.
You are given:
.
.
Take the logarithm of both sides of this equation. You can use base 10 or base e, which is
"ln" or natural logarithms. These can be worked on a normal scientific calculator so either
is a good choice. Let's choose base 10. Taking the Log base 10 of both sides of the equation
results in:
.
.
To simplify things a little, let's use a calculator to find . Enter 625
on the calculator and press the "log" key. You should get 2.795880017. Substituting
this value results in the equation becoming:
.
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Next we'll use another property of logarithms. If you are finding the logarithm of a quantity
that has an exponent, an equivalent form is to multiply the logarithm by the exponent.
In other words, is equivalent to so let's substitute
that into our equation to get:
.
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Now use a calculator to find . Enter 125 and press the "log" key to get . Substitute this into the equation and you now have:
.
.
Finally divide both sides by 2.096910013 and the answer becomes:
. and this is
.
Hope this helps you with your understanding of logarithms.
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