Mathematics, 21.07.2019 04:00 kenoknox

What is 4log1/2^w(2log1/2^u-3log1/2^v written as a single logarithm?

Answers: 2

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Answers

Given:

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)

then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)

Therefore,

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

log of 1/2 (u^2 w^4 / v^3)

Answer from: 10033636

$4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)=\log_{\frac{1}{2}}(\frac{w^4u^2}{v^3})$

Step-by-step explanation:

Given : Expression $4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)$

To write : As a single logarithm?

Solution :

$4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)$

Remove parenthesis,

$=4\log_{\frac{1}{2}}w+2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v$

Simplify each term by applying logarithmic property, $a\log x=\log x^a$

$=\log_{\frac{1}{2}}w^4+\log_{\frac{1}{2}}u^2-\log_{\frac{1}{2}}v^3$

Use the product property of logarithms, $\log_bx+\log_b y=\log_b (xy)$

$=\log_{\frac{1}{2}}w^4u^2-\log_{\frac{1}{2}}v^3$

Use the quotient property of logarithms, $\log_bx-\log_b y=\log_b (\frac{x}{y})$

$=\log_{\frac{1}{2}}(\frac{w^4u^2}{v^3})$

Therefore,

$4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)=\log_{\frac{1}{2}}(\frac{w^4u^2}{v^3})$

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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