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2 years ago

What is the mode of 3 6 9 7 4 6 7 0 7

Mathematics

1 answer:

konstantin123 [22]2 years ago

8 0

Answer:

7 cause mode is the most occurring number

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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,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

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

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

$c) log_b\frac{8}{9}$

By rule 2

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

$d) \frac{log_b27}{log_b16}$

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

2 years ago

If g(x)=−3x+9 g ( x ) = − 3 x + 9 and f(x)=2x+7 f ( x ) = 2 x + 7 , what is the value of g(f(x)) g ( f ( x ) ) ?

olya-2409 [2.1K]

G(f(x)) = g(2x +7) = -3(2x +7) +9 = -6x -21 +9

g(f(x)) = -6x -12

5 0

3 years ago

Lillian has $80 in a savings account. The interest rate is 10%, compounded annually.

arlik [135]

She will have 96.8 dollars in the saving account so she earned 16.8 dollars in interest
If this answered help you then please consider marking it as brainliest to help me level up to expert

5 0

2 years ago

What goes in the highlighted box?

muminat

Answer:

Step-by-step explanation:

Add the 2 like terms on the left

7 0

3 years ago

Read 2 more answers

Can someone help me please?

ladessa [460]