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Chapter 10: Q. 400 (page 1064)

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

log232

Short Answer

Expert verified

The value is 5.

Step by step solution

01

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

Consider the expression log232.

Setting the expression equal to xwe get,

log232=x

And its equivalent exponential form is given as2x=32.

02

Step 2. Compare the exponents

The number 32can be equivalently written as 25. So we get

2x=322x=25

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

x=5

Thus the value oflog232is5.

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