3/4 + 7/15 +5/6 +3/5 +3/20 =

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

Alja [10]

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

<em><u>Solution:</u></em>

Given that,

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

<em><u>Use the following log rules</u></em>

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

A rectangle is 4xcm wide and 2cm long what do you notice

deff fn [24]

The width of the rectangle is twice the length of the rectangle

<h3>How to compare the dimensions of the rectangle?</h3>

The given parameters are:

Width = 4 cm

Length = 2 cm

Express 4 cm as 2 * 2 cm

Width = 2 * 2 cm

Substitute Length = 2 cm in Width = 2 * 2 cm

Width = 2 * Length

This means that the width of the rectangle is twice the length of the rectangle

Hence, the true statement is that the width of the rectangle is twice the length of the rectangle

Read more about rectangles at:

brainly.com/question/25292087

#SPJ1

4 0

1 year ago

Hannah estimated that a bottle could hold 2.2 liters. The actual volume of the bottle was 2 litters. What was the percent error

MrRa [10]

Answer:

I dont have a direct answer but i think i can help.

Step-by-step explanation:

For example, 2%, read "percent", is two every hundred. When we have 100 liters of water, 2% is 2 liters. If we have 200 liters of water, then 2% is 4 liters. Converting a percentage into a fraction can be done by dividing by 100, following the definition of a percentage.

4 0

3 years ago

Which of the following is equivalent to 5/13^3

lys-0071 [83]

Answer:

.00227 or 5/2197

Step-by-step explanation:

following the basic rules of PEMDAS, we know that we have to solve for the exponent first.

so.... 5/2197

as a decimal, this is .00227...

8 0

4 years ago

Morgan scored 41 points in 5 games. How many points would you expect him to make in an 21 game season. Round your answer to the

faust18 [17]

Answer: 172

Step-by-step explanation:

If what I did is right, the answer is 172.2 since 41/5 is 8.2 and I multiply 8.2 times 21, I get 172.2, which rounds to 172.

3 0

3 years ago