Mathematics, 18.11.2019 21:31 smilingntn33p7pqpp

Which expression is equivalent to log subscript w baseline startfraction (x squared minus 6) superscript 4 baseline over rootindex 3 startroot x squared + 8 endroot endfraction?
4 log subscript w baseline startfraction x squared over 1296 endfraction minus one-third log subscript w baseline (2 x + 8)
4 log subscript w baseline (x squared minus 6) minus one-third log subscript w baseline (x squared + 8)
4 log subscript w baseline (x squared minus 6) minus one-third log subscript w baseline (x squared + 8)
4 (log subscript w baseline x squared minus one-third log subscript w baseline (x squared + 8) minus 6)

Answers: 2

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Answers

Answer from: tynitenaire

$4log_w (x^2-6)-\frac{1}{3}log_w (x^2+8)$

Step-by-step explanation:

The expression to simplify is given as:

$L= log_w \frac{(x^2-6)^4}{\sqrt[3]{x^2+8} }$

Using the log property $log_a \frac{x}{y}=log_a x-log_a y$ , we get

$L=\log_w (x^2-6)^4- \log_w \sqrt[3]{(x^2+8)}$

Now, we know that $\sqrt[3]{x} =(x)^{\frac{1}{3}}$ .So,

$\sqrt[3]{(x^2+8)}=(x^2+8)^{\frac{1}{3}}$

Also, property of log is $\log_a x^m=mlog_a x$

Using the above properties, we get

$L=\4\log_w (x^2-6)- \frac{1}{3}\log_w (x^2+8)$

Hence, the given expression is equivalent to $\4\log_w (x^2-6)- \frac{1}{3}\log_w (x^2+8)$

Answer from: meeks7442

Option C on E2020

Step-by-step explanation:

$Which expression is equivalent to log subscript w baseline startfraction (x squared minus 6) supersc$

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

Use a paragraph, flow chart, or two-column proof to prove the angle congruency. given: ∠cxy ≅ ∠bxy

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Which expression is equivalent to log subscript w baseline startfraction (x squared minus 6) supersc...