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Chapter 10: Q. 10.42 (page 1024)

Find the exact value of each logarithm without using a calculator:

a)log981b)log82c)log319

Short Answer

Expert verified

Part (a) The value of the logarithm is 2.

Part (b) The value of the logarithm is 13.

Part (c) The value of the logarithm is-2.

Step by step solution

01

Step 1. Given information.

The given logarithms are

a)log981b)log82c)log319

02

Step 2. Solving part (a).

Consider the given expression,

log981=x

Now, we will convert the given expression to exponential form and simplify.

log981=x9x=819x=92x=2

Hence, the value of the logarithm is2.

03

Step 3. Solving part (b).

Consider the given expression,

log82=x

Now, we will convert the given expression to exponential form and simplify.

log82=x8x=223x=223x=213x=1x=13

Hence, the value of the logarithm is13.

04

Step 4. Solving part (c).

Consider the given expression,

log319=x

Now, we will convert the given expression to exponential form and simplify.

log319=x3x=193x=1323x=3-2x=-2

Hence, the value of the logarithm is-2.

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