Question
Let x = log_2 1/8
Write the exponential form of the equation and solve the equation for x.
Write the exponential form of the equation and solve the equation for x.
Answers
MathMate
Here are a few hints:
a.a.a = a³
(1/a).(1/a).(1/a) = a<sup>-3</sup>
log<sub>a</sub> a<sup>b</sup> = b
For example:
log<sub>10</sub>100 = log<sub>10</sub>10² = 2
a.a.a = a³
(1/a).(1/a).(1/a) = a<sup>-3</sup>
log<sub>a</sub> a<sup>b</sup> = b
For example:
log<sub>10</sub>100 = log<sub>10</sub>10² = 2
Pamela
2x = 2^log2(1/8)
2x = (1/8)
Are these acceptable answers?
2x = (1/8)
Are these acceptable answers?
MathMate
You're getting there, but not exactly yet.
Try writing
1/8
= 1/2³
= 2<sup>-3</sup>
and apply one of the above identities given in the hint.
Try writing
1/8
= 1/2³
= 2<sup>-3</sup>
and apply one of the above identities given in the hint.
Pamela
Does this work? Thanks!
Exponential form is 2^-3=1/8
To Check:
2^-3=1/2^3=1/8
Exponential form is 2^-3=1/8
To Check:
2^-3=1/2^3=1/8
MathMate
So far so good, but you have to continue to solve for x, such as:
x = log<sub>2</sub>2<sup>-3</sup>
How does that compare with the identity above:
log<sub>a</sub> a<sup>b</sup> = b
x = log<sub>2</sub>2<sup>-3</sup>
How does that compare with the identity above:
log<sub>a</sub> a<sup>b</sup> = b
MathMate
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.
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.