Asked by Pamela
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
Answered by
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
Answered by
Pamela
2x = 2^log2(1/8)
2x = (1/8)
Are these acceptable answers?
2x = (1/8)
Are these acceptable answers?
Answered by
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.
Answered by
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
Answered by
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
Answered by
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.
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