Question

smlifiry the following ​

Answer 1

Solution

Given :-

• log (145/8) - 3log (3/2) + log (54/29)

Explanation

We know some important formula

★ log (x/y) = log x - log y .

★ log x ^n = n log x.

★ log xy = log x + log y .

So, Now calculate

= log (145/8) - 3log (3/2) + log (54/29)

Use Formula

( log (x/y) = log x - log y .)

= log 145 - log 8 - 3 (log 3 - log 2) + log 54 - log 29

Use Formula

( log x^n = n log x )

= log (5 × 29) - log 8 - log 3³ + log 2³ + log (27 × 2) - log 29

Use Formula

( log xy = log x + log y )

= log 5 + log 29 - log 8 - log 27 + log 8 + log 27 + log 2 - log 29

Here,

( log 29 , log 27 & log 8 are cancel )

= log 5 + log 2 .

Value of log 5 & log 2 by log table .

★ log 2 = 0.3010

★log 5 = 0.6989

Keep above value,

= 0.6989 + 0.3010

= 0. 9999 [ Ans.]

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Note:-

† We calculate log value by taking base on 10 .

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Answer 2

Step-by-step explanation:

See the attachment

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