Question

Please solve the attached question.

•Don't spam ​

Answer 1

Secrets,
Here we go,



we have,
$log_{a}(x) = \frac{1}{ \alpha } \\ log_{b}(x) = \frac{1}{ \beta } \\ log_{c}(x) = \frac{1}{ \gamma }$


And as the hint has already distracted me ,
all we need to get the answer of,
$log_{abc}(x)$

is to solve the following,
$\frac{ logx }{ log a+ log b + log c }$


I'll do the simplest thing in human history aka subsitution for log a log b and log c from the data given in questions.

Let's exapand the data a bit for our comfort,
(which to my annoyance has already been done I mean like why can't they do this with tougher questions =_= I solve. It kills excitement brav.)

$\frac{ logx }{ loga } = \frac{1}{ \alpha } \\ \\ \frac{ logx }{ logb } = \frac{1}{ \beta } \\ \\ \frac{ logx }{ logc } = \frac{1}{ \gamma }$


Moving on to substituion,

$\frac{ logx }{ \alpha logx + \beta logx + \gamma logx} \\ \\ = \frac{ logx}{ log x( \alpha + \beta + \gamma ) }$

I don't think you need my help after this but I'm gonna do it anyways (my reported answers)

we have,
The answer as,
$\frac{1}{ \alpha + \beta + \gamma }$



Finally you're done here and so I am with my chit chat.

Cheers!

Answer 2

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