Hi there.
Here’s another catch-the-error video.
As always, I will do a calculation
which contains a mistake.
It’s up to you to see where I make this mistake.
We will solve the following equation:
log base 2 of (x+1)^2 equals 6.
First we can simplify this equation
using the rules of calculation for logarithms.
We can take the exponent out of the logarithm.
2 times the log (base 2) of (x+1) equals 6.
Now we divide both sides by 2.
The log (base 2) of (x+1) equals 3.
And using the definition of the logarithm in base 2,
we find that (x+1) = 2^3 = 8,
so x = (8-1) = 7.
We can check that this is indeed
a solution of our equation.
The log (base 2) of (7+1)^2
equals the log (base 2) of 8^2,
equals the log (base 2) of 64,
equals the log (base 2) of 2^6,
is 6.
So, we simplified the equation,
solved it, and checked the solution.
But actually, this is not the only solution of our equation,
there is another one!
Can you find the solution?
And do you know why we missed it here?
