Welcome back to speller tutorial services. We're going to talk about exponential equations today an
Exponential equation is an equation where a variable exists in the exponent or power and in our example here
We see that. We have a base of 2
Being raised to the x plus 1 power and that's equal to 9 the power of x plus 1
Because there's an extent we know that this here is an exponential equation
Normally the first thing we want to try to do in an exponential equation is try to get like basis
But we see here that when we factor 9 the factors are nine or 13 and nine
so we're not going to be able to factor 9 to get a
Light base of 2 so our next option is to take the log or natural log of both sides of this particular equation
We're going to do the natural log of both sides
so the left-hand side is becomes the natural log, and that's just Ln of
2 raised to the x + 1 power is equal to
the natural log of 9 to be a little clearer Emma put this [x] [plus] 2 I'm sorry x plus 1 and
Parentheses now, we're going to use some of the rules for dealing with
logs first rule is that if I have a number raised to a power that power comes out front and
That power is then multiplied by whatever we're taking the natural log of in this case
We're multiplying x plus 1 times the natural log of 2 and then we rewrite the right hand side
Which is natural log of nine now?
we're going to try to iSolate x
Since these two terms here are being joined by multiplication. We know that we can divide both sides by the natural Log of 2
natural log of 2 divided by the natural log of 2 simplifies down to one and
that just leaves us with x plus 1 is equal to the natural log of 9
divided by the natural Log of 2
This point we're going to go ahead [and] subtract 1 from both sides
that's going to leave us with x is equal to the natural log of 9
and log of 2
minus 1
We're going to call the power calculator here
because we're going to find out what the approximate value of x should be one go ahead and clear a
Calculator we want to do
press nine take the natural log of that
divide that value by
To take the natural log of that
Equals and I want to subtract one off of that and we see that comes out to be 2 point 1
69 we're going to round that to approximately two point
17
So we can say here that this here is approximately two point 17
which be the value of x
All right that sums it up for this video on exponential equations
Please visit the spell tutorial channel on YouTube and thank you for watching
