MATHEMATICS COLLEGE

Find the numerical value of the log expression HELP PLS

Answers

Answer 1

Answer:

The value of $\rm{log\ 10^(19)$ is 19.

Logarithm

A log function is a way to find how much a number must be raised in order to get the desired number.

$a^c=b$

can be written as

$\rm{log_ab=c$

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

$\rm{log\ 1000 = 3$

Given to us

log a = 3,

log b = 4,

log c = -1,

Logarithm Values

log a = 3

$10^3 = a\n1000 = a\na=1000$

lob b = 4,

$10^4=b\n10000=b\nb=10,000$

log c = -1,

$10^(-1) = c\n\n(1)/(10) = c\n\nc = 0.1$

Simplifying

$\rm{log(b^7)/(a^5c^6)\n$

$=\rm{log(10,000^7)/(1,000^5* 0.1^6)\n$

$=\rm{log 10^(19)$

Hence, the value of $\rm{log\ 10^(19)$ is 19.

Answer 2

Answer:

Step-by-step explanation:

Given:

$(b^7)/(a^5c^6)$

log a = 3,

log b = 4,

log c = -1

Required:

Numerical value of the log expression

SOLUTION:

To solve this, we need to recall the rules to apply in each step:

$(b^7)/(a^5c^6)$

Step 1: Apply log of quotients => i.e. $log (a)/(b) = log(a) - log(b)$

$log(b^7) - (log(a^5c^6))$

Step 2: Apply log of products. i.e. log ab = log a + log b.

$log(b^7) - (log(a^5) + log(c^6))$

Step 3: Apply log of exponents. i.e. $log(a^n) = nlog(a)$ .

$7log(b) - (5log(a) + 6log(c))$

Step 4: Substitute log a = 3, log b = 4, log c = -1, into the equation.

$7(4) - (5(3) + 6(-1))$ .

$28 - (15 - 6)$ .

$28 - 9$ .

$= 19$ .

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Share £360 in the ratio 2:7

Answers

Answer:

80:280

Step-by-step explanation:

Final answer:

To share £360 in the ratio 2:7, you first find the value of one part by dividing £360 by the total number of ratio parts (9). Then, multiply each part of the ratio by this amount, resulting in £80 and £280.

Explanation:

To share £360 in the ratio 2:7, you first need to understand that the sum of the parts of the ratio (2+7) equals to 9 parts. The amount of £360 should be distributed into these 9 parts.

First, you divide the total amount by the total number of parts:
£360 / 9 = £40.

This result £40 is the value of 1 part. To find the amounts for the ratio 2:7, you multiply each part of the ratio by the value of 1 part:

2 * £40 = £80 which is the amount for the first part of the ratio, and
7 * £40 = £280 which is the amount for the second part of the ratio.

Learn more about Ratios here:

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What is 743x295
What do I need to d

Answers

Answer: 219,185

-Multiply the place values to find the answer,

Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

Answers

Answer:

$e^(3t)(2t+5t^(2))$

Step-by-step explanation:

$L^(-1)[(2s+4)/((s-3)^(3)) ]=$

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem: $L^(1) [F(s-a)=L^(-1)[F(s)|_(s \to s-a)\n L^(1) [F(s-a)=e^(at) f(t)$

$L^(-1)[(2s+4)/((s-3)^(3)) ]=e^(3t) L^(-1)[(2(s+3)+4)/(s^(3)) ]$

Separate the fraction in a sum:

$e^(3t) L^(-1)[(2s+10)/(s^(3)) ]=e^(3t) L^(-1)[(2s)/(s^(3))+(10)/(s^(3)) ]=e^(3t) (L^(-1)[(2)/(s^(2))]+ L^(-1)[(10)/(s^(3))])$

The formula for this is:

$L^(-1)[(n!)/(s^(n+1)) ]=t^(n)$

Modify the expression to match the formula.

$e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ (10)/(2) L^(-1)[(2)/(s^(2+1))])=e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])$

Solve

$e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])=e^(3t)(2t+5t^(2) )$

A farm stand wants to sell fruit to local grocery stores in packages withbaskets of apples, worth $10 apiece, and baskets of peaches, worth $13
apiece. The owner wants each package to include 50 baskets total, and he
wants to sell each package for $566. How many baskets of apples and how
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A. 10 apples, 13 peaches
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C. 28 apples, 22 peaches
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Answers

Answer:

28 apples and 22 peaches

Step-by-step explanation:

Is the percent increase from 50 to 70 equal to the percent from 70 to 50explain.

Answers

Answer:

20/50=40% So 50 to 70 percent increase is 40%.

20/70=about 28.57% decrease for 70 to 50.

So they aren't the same because the hundred percent are different numbers in this case.

Find the distance between the two points

Answers

I got 8.1 units
.
I used the Pythagorean Theorem to find my answer. I plugged in 7 for the long side and 4 for the short side and then solved.
.
Hope this helps :)

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