We want to evaluate each logarithm
on a calculator, round
to four decimal places,
and then write the related
exponential equation.
For number one, we have
log base two of 823.
Most calculators only have buttons
for natural log or log base e,
as well as common log or log base 10.
And therefore, on most calculators,
to evaluate log base two of 823,
we would need to use the
change of base formula.
This is not the case for the TI-84.
The TI-84 has a special log feature
that allows us to enter any base we wish.
From the home screen, we press Math,
and select option A
by either pressing the
up arrow or down arrow.
Let's press the up arrow
until we highlight option A,
which is logBASE, press enter.
Notice we can enter any base we want,
which in this case is two, right arrow.
The number or input is 823, enter.
To four decimal places, we have 9.6847.
So this is an approximate
value because it is rounded.
Let's just verify we get the same result
using the change of base
formula shown below.
And for this first example,
let's use the change of base
formula with natural log,
which means log base b of
x is equal to natural log x
divided by natural log b,
or in our case, natural log
823, closed parenthesis,
divided by natural log two,
which does give us the same result.
And after the exponential
equation, remember,
a logarithm is an exponent.
The related exponential equation
is two raised to the power of 9.6847
is approximately 823.
And let's go ahead and verify this.
Notice how we do have approximately 823.
It's a little less,
because we did round down.
Next, we have log base 1/2 of 0.78.
Going back to the calculator,
again, we press Math,
and then option A for logBASE, enter.
The base is 1/2, so one
divided by two, right arrow.
The input, our number is 0.78, enter.
To four decimal places, we have 0.3585.
Let's verify this using
the change of base formula.
This time using common log, and therefore,
log base 1/2 of 0.78
is equal to common log 0.78,
closed parenthesis,
divided by common log 1/2.
And of course, we do get the same result.
The related exponential equation is 1/2
raised to the power of 0.3585
is approximately 0.78.
And again, let's verify this.
And notice how we do
get approximately 0.78.
Number three, notice how
there's no base given,
and therefore, we know it's
just common log or log base 10,
and therefore, we can just
use the common log button
from the home screen.
We simply press Log, 1,237,
closed parenthesis, and enter.
To four decimal places, we have 3.0924.
The related exponential equation is 10
raised to the power of 3.0924
is approximately 1,237.
And again, let's verify.
And we do get approximately 1,237.
For number four, we have natural log 72.
The natural log button
is on the home screen.
We enter natural log 72,
closed parenthesis, and enter.
To four decimal places, we have 4.2767.
And again, natural log is log base e.
The related exponential equation is e
raised to the power of 4.2767
is approximately 72.
And let's also verify this.
If we press second natural log,
this brings up e to the power of,
and we simply enter the exponent,
which does give us approximately 72.
I hope you found this helpful.
