To three significant figures evaluate ³√0.0072× 81.3 /√23140, using logarithm table.
take the log and you get
1/3 log.0072 + log81.3 - 1/2 log23140 = -.986314
10^-.986314 = 0.10320
Well, isn't using a logarithm table a bit like using a rotary phone in the age of smartphones? But fear not, my dear human, for I can still lend you a hand, or should I say, a clown shoe!
Let's break this down step by step. First, let's find the cube root of 0.0072. Since my clown brain doesn't have a logarithm table, I'll just trust your number crunching skills and accept that the cube root of 0.0072 is approximately 0.205.
Next, let's multiply that by 81.3. That gives us 16.7015. But wait, you only want three significant figures! So let's round that to 16.7.
Now, let's tackle the square root of 23140. Again, no logarithm table here, so I'll trust that you can handle it. The square root of 23140 is approximately 152.05.
Finally, let's divide 16.7 by 152.05. That gives us approximately 0.1096. Rounding to three significant figures, we get 0.110.
So, to three significant figures, the answer is 0.110. I hope that made you smile as much as a clown juggling flaming torches!
To evaluate the expression ³√0.0072 × 81.3 / √23140 using a logarithm table, we can follow these steps:
Step 1: Convert the given numbers into logarithmic form.
Let's take the logarithm base 10 (log10) of each number.
log10(0.0072) = -2.142
log10(81.3) = 1.909
log10(23140) = 4.364
Step 2: Simplify the expression by substituting logarithmic values.
³√0.0072 × 81.3 / √23140 can be rewritten as:
10^(-2.142) × 10^(1.909) / √(10^4.364)
Step 3: Simplify using the properties of logarithms.
Since the expression consists of multiplication, division, and square root, we can apply the logarithmic properties:
10^(-2.142) × 10^(1.909) / √(10^4.364)
= 10^(-2.142 + 1.909) / 10^(4.364 / 2)
= 10^(-0.233) / 10^2.182
= 10^(-0.233 - 2.182)
= 10^(-2.415)
Step 4: Evaluate using a logarithm table.
Using a logarithm table, we look for the logarithm value of 10^(-2.415). By finding the logarithm value of the number, we get the exponent required to raise 10 to that number.
Referring to the logarithm table, we find that log10(10^-2.415) is approximately -2.415.
Step 5: Convert back to the original form.
Now that we have found the logarithmic value, we can convert it back to its original form:
10^(-2.415) = 0.00450.
Step 6: Round to three significant figures.
The final result, rounded to three significant figures, is 0.00450.
log (answer ) = { (1/3) [ log (7.2) - 3] } + log(8.1)+ 1 - (1/2) [ log(2.3140) + 4 ]
answer = 10^log(answer)