Let x = log_2 1/8
Write the exponential form of the equation and solve the equation for x.
Here are a few hints:
a.a.a = a³
(1/a).(1/a).(1/a) = a-3
loga ab = b
For example:
log10100 = log1010² = 2
2x = 2^log2(1/8)
2x = (1/8)
Are these acceptable answers?
You're getting there, but not exactly yet.
Try writing
1/8
= 1/2³
= 2-3
and apply one of the above identities given in the hint.
Does this work? Thanks!
Exponential form is 2^-3=1/8
To Check:
2^-3=1/2^3=1/8
So far so good, but you have to continue to solve for x, such as:
x = log22-3
How does that compare with the identity above:
loga ab = b
Exponential form is 2^-3 = 1/8 This isn't correct?
This part is correct, that's the "so far so good" part. Sorry if there was a misunderstanding.
You also need to do the second part: " and solve the equation for x."
You are very close to finishing, keep it up.
To write the exponential form of a logarithmic equation, you need to understand the basic relationship between logarithms and exponentiation.
The logarithm is the inverse operation of exponentiation. It tells you the exponent that you need to raise a particular base to in order to get a given number.
In this case, you have
x = log_2(1/8)
To write this in exponential form, you would use the definition of logarithms. The base of the logarithm (2 in this case) is raised to the power of the logarithm (x), which should equal the argument of the logarithm (1/8).
2^x = 1/8
Now, we need to solve this equation for x.
To do that, we can rewrite 1/8 as a power of 2.
1/8 = 2^(-3)
Now, substitute 2^(-3) into the equation.
2^x = 2^(-3)
Since the bases are the same, the powers must be equal.
x = -3
So, the solution of the equation is x = -3.