Question

Hi . i'm kinda stuck on this question .
Any help will be appreciated.
Please show workings ;
Solve the following expressions using laws of logarithm and using antilogarithm ;
1.$\sqrt{69.5^2-30.5^2}$
2. $\frac{371.2^\frac{1}{3}\times 76500 }{1125 \times 0.012}$

Answer 1

Answer:

1. 62.44998
2. 40725.2396667

Step-by-step explanation:

• Refer to https://brainly.com/question/17913554 for the formulas and the method if not clear here

1.................................................

• √69.5^2 - 30.5^2 =
• √(69.5+30.5)((69.5- 30.5) =
• √100*39 =
• 10√39 =
• antilog (log (10√39)) =
• antilog (1 + 1/2 log 39)=
• antilog (1 + 1/2*1.59106460703) =
• antilog (1.79553230351) =
• 62.44998

2..................................................

• 371.2^(1/3)×76500/(1125×0.012) =
• 371.2^(1/3)×76500/13.5 =
• 371.2^(1/3) × 5666.66666667

Solving the first part

• antilog (log (371.2^(1/3))) =
• antilog (1/3 log(371.2)) =
• antilog (1/3*2.56960796755) =
• antilog (0.85653598918) = 7.186807

Continuation

• 7.186807× 5666.66666667 = 40725.2396667

Note. the numbers are not rounded

Hope it helps.