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mathmath333
 one year ago
logarithm question
mathmath333
 one year ago
logarithm question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0solve \(\large \color{black}{\begin{align} \log_{10}(x^{3}+5)=3\log_{10}(x+2)\hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & (a.)\ \dfrac{2+\sqrt2}{2} \hspace{.33em}\\~\\ & (b.)\ \dfrac{2\sqrt2}{2} \hspace{.33em}\\~\\ & (c.)\ \text{both a.) and b.) } \hspace{.33em}\\~\\ & (d.)\ \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4\[\log_{10}(x^3 + 5) = \log_{10}{(x+2)^3}\]\[\Rightarrow x^3 + 5 = x^3 + 6x^2 + 12x + 8\]\[\Rightarrow 6x^2 + 12x + 3 = 0 \]Choose the solution for which both logarithms are defined.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0my book has given option d.)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4If you know that your answer is correct, why care about the book?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i dont have brains

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4You're correct. Don't worry.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0all options of book is correct except this ? suspictious

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4Book bhi ek insaan ne hi likhi hai. As I said, your answer is correct.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you may double check with wolfram

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0wolfram gave this http://www.wolframalpha.com/input/?i=solve+%5Clog_%7B10%7D%28x%5E%7B3%7D%2B5%29%3D3%5Clog_%7B10%7D%28x%2B2%29+over+reals&dataset=

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0ok thnx, by the way is there a condition like \(x^{3}+5>0\) and \((x+2)^{3}>0\)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4Yes, which is what I meant that the logarithms should be defined. Both roots satisfy both conditions.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0how do i find value of \(5^{1/3}\) by pen paper to check

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4You don't need to find the value of \(5^{1/3}\). Plug in \(1.4 \) for \(\sqrt 2\) and that should almost always work.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0y i dont need that value

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4You need to check if \(x^3 + 5 > 0\) and \(x+2>0\). The second one is easier than the first. The solutions you get are\[\frac{2 + \sqrt 2}{2} \approx  0.3 , \frac{2  \sqrt 2}{2} \approx 1.7 \]The second one is simple. The first condition, well, is satisfied the first root. The second root is a closer call but it satisfies the condition.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4satisfied for the first root*

phi
 one year ago
Best ResponseYou've already chosen the best response.1You are the victim of a typo.... it happens quite a bit in math books because it is very hard to check the answers....

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0no typo for x^3+5>0

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.4He's talking about the answerkey.
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