The document shows the step-by-step working of solving the logarithmic expression (780.6)^(1/2) x 3.000 / 4.000. It involves breaking the expression into individual logarithmic terms, applying logarithmic rules to simplify, and then taking the antilogarithm of the final expression to obtain the numerical value of 12.10.

1. 1) In log Multiply change into Addition
2) In log Divide change into subtraction
3) In log we never find power
4) Characteristics = value – 1
5) log 1 = 0
6) log 10 = 1
Key point of logarithm
LOGARITHM

2. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎

3. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)

4. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
In this step
We know that the
square root is
equal to the half
power means ½.
So we remove
square root in
addition of ½.

5. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)

7. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)

8. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)
𝟏
𝟐
(2.8924) +
𝟏
𝟐
(0.4771) – (0.6021)

9. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)
𝟏
𝟐
(2.8924) +
𝟏
𝟐
(0.4771) – (0.6021)
1.4462 + 0.2385 – 0.6021
1.0826

10. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)
𝟏
𝟐
(2.8924) +
𝟏
𝟐
(0.4771) – (0.6021)
1.4462 + 0.2385 – 0.6021
1.0826
For Antilog
0826

12. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)
𝟏
𝟐
(2.8924) +
𝟏
𝟐
(0.4771) – (0.6021)
1.4462 + 0.2385 – 0.6021
1.0826
For Antilog
0826
1208 + 2
1210

13. EXERCISE 3.6
 Find the value of the following by using logarithms:
8)
(𝟕𝟖𝟎.𝟔)
𝟏
𝟐 𝑿 𝟑.𝟎𝟎𝟎
𝟒.𝟎𝟎𝟎
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log ( 𝟑. 𝟎𝟎𝟎) – log (𝟒. 𝟎𝟎𝟎)
Log (𝟕𝟖𝟎. 𝟔)
𝟏
𝟐 + log (𝟑. 𝟎𝟎𝟎)
𝟏
𝟐 – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
Log (780.6) +
𝟏
𝟐
log (3.000) – log (𝟒. 𝟎𝟎𝟎)
𝟏
𝟐
(2.8921 + 3) +
𝟏
𝟐
(0.4771 + 0) – (0.6021 + 0)
𝟏
𝟐
(2.8924) +
𝟏
𝟐
(0.4771) – (0.6021)
1.4462 + 0.2385 – 0.6021
1.0826
For Antilog
0826
1208 + 2
12.10