Unit Test: A

If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

Solution:

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

Use the following log rules

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

3 years ago

Many Irish-Catholic and Chinese immigrants helped improve the infrastructure of the

alekssr [168]

Answer:

The Transcontinental Railroad

Step-by-step explanation:

Hope it helps you :)

5 0

3 years ago

Read 2 more answers

Pls help me this is due tomorrow

Anna [14]

Step-by-step explanation:

Claim: There's 14 Goats and 9 Chickens!!

Data:

Working with the Provided Information.

Let the Number of goats be x

let the Number of Chickens be y

x + y = 23..... (i)

Since the goat Possesses Two Pair of Legs... Which is a Total of 4 Legs... We say Let its Contribution be 4x.

The Chicken has Only a Pair Of Legs...Which is a total of 2 legs.... We say let its contribution be 2y

4x + 2y = 74 .....(ii)

BRINGING BOTH EQUATIONS TOGETHER.

x + y = 23

4x + 2y = 74

From Eqn i

x= 23 - y

Substitute into eqn ii

4(23 - y ) + 2y = 74

92 - 4y + 2y = 74

92 - 2y = 74

2y = 92 - 74

2y = 18

y= 9.

Substitute y into any of the eqns to get x

x + y = 23

x + 9=23

x = 23 - 9

x = 14

This simply proves that there are 14 Goats and 9 Chickens!!!.

HAVE A GREAT DAY!

7 0

3 years ago

Keisha is babysitting at $8 per hour to earn money for a car. So far she has saved $1300. The car that Keisha wants to buy costs

11Alexandr11 [23.1K]

Answer:

$4100

Step-by-step explanation:

For Kaisha to get this car we have these information available

Amount saved = $1300

The cost of the car = $5400

Let The amount left to complete the car = k

We have this equation

K + $1300 = $5400

K = 5400 - 1300

K = 4100

Therefore Kaisha still needs to earn an additional amount of $4100 for the total amount of the car to be completed.

5 0

3 years ago

302 + 12 M equals 278

slavikrds [6]

In the given question there is an equation that has to be solved and the value of the unknown variable "M" has to be determined. It is absolutely possible to find the exact value of the variable "M" as there is 1 equation and 1 variable.
302 + 12 M = 278
12 M = 278 - 302
12 M = - 24
M = - (24/12)
= - 2
So the value of the unknown variable "M" comes out to be -2. I hope the procedure is clear enough for you to understand and also this is the answer you were looking forward to.

8 0

3 years ago

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