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Chapter 5: Q 110. (page 309)

Show that loga1N=-logaNwhere a and N are positive real numbers and a鈮�0.

Short Answer

Expert verified

It is proved that loga1N=-logaNwhere a and N are positive real numbers and a鈮�1.

Step by step solution

01

Step 1. Identifying the property.

To show that loga1N=-logaN.

Here we can use the property of logarithm, logaMN=logaM-logaN, hereM=1&N=N.M=1&N=N

02

Step 2. Applying the property.

Applying the property of logarithm,

loga1N=loga1-logaN.

Since loga1=0, the equation becomes,

loga1N=0-logaN=-logaN

Hence it is proved.

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