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Question 1 of 4
Derive the Change of Base formula from the general equation
x=logaN
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Logarithmic Form
x=logaN
Transform the general logarithmic equation to exponent form
x |
= |
logaN |
N |
= |
ax |
Insert logarithms of the same base to both sides, then solve for x
N |
= |
ax |
logbN |
= |
logbax |
logbN |
= |
logbax |
logbN |
= |
xlogba |
logbxp=plogbx |
logbN÷logba |
= |
xlogba÷logba |
Divide both sides by logba |
|
logbNlogba |
= |
x |
|
x |
= |
logbNlogba |
Also, remember that, x=logaN
Hence, the Change of Base formula is: logaN=logbNlogba
logaN=logbNlogba
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Question 2 of 4
Evaluate using Change of Base
log29
Round answer to 5 decimal places
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Logarithmic Form
x=logaN
Use the change of base formula, then use the calculator to solve the logarithm
log29 |
= |
log109log102 |
Calculators use 10 as base for the log function |
|
|
= |
3.16993 |
Compute using the calculator |
log29=3.16993
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Question 3 of 4
Solve for x using Change of Base
5x=11
Round answer to 4 decimal places
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Logarithmic Form
x=logaN
Transform the given exponential equation to logarithmic form
5x |
= |
11 |
x |
= |
log511 |
Use the change of base formula, then use the calculator to solve the logarithm
x |
= |
log511 |
|
x |
= |
log1011log105 |
Calculators use 10 as base for the log function |
|
x |
= |
1.4899 |
Compute using the calculator |
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Question 4 of 4
Solve for x using Change of Base
2x=0.062
Round answer to 4 decimal places
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Logarithmic Form
x=logaN
Transform the given exponential equation to logarithmic form
2x |
= |
0.062 |
x |
= |
log20.062 |
Use the change of base formula, then use the calculator to solve the logarithm
x |
= |
log20.062 |
|
x |
= |
log100.062log102 |
Calculators use 10 as base for the log function |
|
x |
= |
−4.0116 |
Compute using the calculator |