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Write as a Single Log
When solving log equations, you might need to rewrite a log expression with the same base as a single log.
Log of Power and Log of Product Properties
The example below contains the addition of two logs.
You are asked to rewrite this as a single log.
Process
~ This is the product of the Power and the log: 4 loga 3
~ Apply the Log of a Power property.
~ 4 is the exponent of log 3 43
~ 43 = 81
~ We have the Sum of the logs, which equals the Log of a Product.
~ In this case, multiply the integers to obtain the final single log.
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Log of Power and Log of Quotient Properties
The example below contains the difference of two logs.
You are asked to rewrite this as a single log.
Process
~ This is an example of the quotient of a Power and a log.
~ Apply the Log of a Power property to both expressions. ln 82/3 34 = 81
~ Simplify the numeric expressions.
ln 4 - ln73
~ We have the Difference of the Logs, which equals the Log of a Quotient.----------------
Log of Product and Log of Quotient
The example below contains the power, difference, and sum of logs.
Process
~ The sum of log x and log 9 becomes the Sum of Two logs.
~ Apply the Log of a Product log(9x)
~ There is another sum of two logs
log (9x) and log (x2 + 1)
~ Apply the Log of a Product
log(9x)(x2 + 1)
~ We are left with the difference of two logs log(9x)(x2 + 1) and log 5
~ Apply the Log of a Quotient
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