Pre-Calculus › Exponential and Logarithmic Functions
Solve:
None of the other answers.
Combine the constants:
Isolate the exponential function by dividing:
Take the natural log of both sides:
Finally isolate x:
Solve for .
First, let's begin by simplifying the left hand side.
becomes
and
becomes
. Remember that
, and the
in that expression can come out to the front, as in
.
Now, our expression is
From this, we can cancel out the 2's and an x from both sides.
Thus our answer becomes:
.
Solve for .
First, let's begin by simplifying the left hand side.
becomes
and
becomes
. Remember that
, and the
in that expression can come out to the front, as in
.
Now, our expression is
From this, we can cancel out the 2's and an x from both sides.
Thus our answer becomes:
.
Solve:
None of the other answers.
Combine the constants:
Isolate the exponential function by dividing:
Take the natural log of both sides:
Finally isolate x:
Solve for .
First, let's begin by simplifying the left hand side.
becomes
and
becomes
. Remember that
, and the
in that expression can come out to the front, as in
.
Now, our expression is
From this, we can cancel out the 2's and an x from both sides.
Thus our answer becomes:
.
Solve:
None of the other answers.
Combine the constants:
Isolate the exponential function by dividing:
Take the natural log of both sides:
Finally isolate x:
Solve the equation for .
The key to this is that . From here, the equation can be factored as if it were
.
and
and
and
Now take the natural log (ln) of the two equations.
and
and
Solve the equation for .
The key to this is that . From here, the equation can be factored as if it were
.
and
and
and
Now take the natural log (ln) of the two equations.
and
and
Solve the equation for .
The key to this is that . From here, the equation can be factored as if it were
.
and
and
and
Now take the natural log (ln) of the two equations.
and
and
Completely expand this logarithm:
The answer is not present.
We expand logarithms using the same rules that we use to condense them.
Here we will use the quotient property
and the power property
.
Use the quotient property:
Rewrite the radical:
Now use the power property: