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Question 1 of 4
Solve for N
log5N=−3
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Logarithmic Form
logaN=x
Convert the equation to exponent form by first identifying the components
logaN |
= |
x |
log5N |
= |
−3 |
N |
= |
N |
a |
= |
5 |
x |
= |
−3 |
Substitute the components into the exponent form
Solve for the value of N
N |
= |
5−3 |
|
N |
= |
153 |
Reciprocate 5−3 |
|
N |
= |
1125 |
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Question 2 of 4
Solve for N
log3N=−4
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Logarithmic Form
logaN=x
Convert the equation to exponent form by first identifying the components
logaN |
= |
x |
log3N |
= |
−4 |
N |
= |
N |
a |
= |
3 |
x |
= |
−4 |
Substitute the components into the exponent form
Solve for the value of N
N |
= |
3−4 |
|
N |
= |
134 |
Reciprocate 3−4 |
|
N |
= |
181 |
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Question 3 of 4
Solve for a
loga27=3
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Logarithmic Form
logaN=x
Convert the equation to exponent form by first identifying the components
logaN |
= |
x |
loga27 |
= |
3 |
N |
= |
27 |
a |
= |
a |
x |
= |
3 |
Substitute the components into the exponent form
Solve for the value of a
27 |
= |
a3 |
3√27 |
= |
3√a3 |
Find the cube root of both sides |
3 |
= |
a |
a |
= |
3 |
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Question 4 of 4
Solve for x
logbx=3logb2+logb4
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Remove the coefficient from the second term
logbx |
= |
3logb2+logb4 |
logbx |
= |
logb23+logb4 |
logbxp=plogbx |
logbx |
= |
logb8+logb4 |
logbx |
= |
logb8+logb4 |
logbx |
= |
logb(8)(4) |
logbxy=logbx+logby |
logbx |
= |
logb32 |
Since the bases of both sides are the same, the logarithm can be dropped
logbx |
= |
logb32 |
x |
= |
32 |