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Chapter 10: Q. 402 (page 1064)

In the following exercises, find the exact value of each logarithm without using a calculator.

log319

Short Answer

Expert verified

The value is -2.

Step by step solution

01

Step 1. Form a logarithmic equation and write its equivalent exponential form  

Consider the expression log319.

Setting the expression equal to xwe get,

log319=x

And its equivalent exponential form is given as 3x=19.

02

Step 2. Compare the exponents  

The number 19can be equivalently written as 3-2. So we get

3x=193x=3-2

Now, as the base is the same, so on comparing the exponents we get

x=-2

Thus the value of log319is -2.

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