Author Topic: logarithmic functions question help (Read 1850 times) Tweet Share

tolga · « **on:** December 30, 2009, 05:37:18 pm »

Q2)Solve for x in the following
a)(log5(x))^2 - log5(x^3) =2=0 b)log2(x^4)=(log2(x))^2 c)log10(x^2=2x-5)=1
Note:Assume the the number after log is to the pwer bolow log.

brightsky · « **Reply #1 on:** December 30, 2009, 06:17:24 pm »

Can you make your equations a bit more clearer? There are more than one equals sign in them. :p

tolga · « **Reply #2 on:** December 30, 2009, 07:15:45 pm »

Solve for x in the following:
A)(log3(x))^2-log3(x^4)+3=0 B)log3(x^3)=(log3(x))^2 C)log3(x^2-3x-7)=1 D)log10(x)/log10(2)=4
Note: In thes questions the number after log is to the power below log.

superflya · « **Reply #3 on:** December 30, 2009, 07:18:54 pm »

hurts my eyes just looking at it. latex

Aden · « **Reply #4 on:** December 30, 2009, 07:30:11 pm »

You could at least seperate A, B, C and D...

brightsky · « **Reply #5 on:** December 30, 2009, 07:37:14 pm »

Are these new ones lol?
Anyway, see how I go...

a)
$log^2_3 x - log_3(x^4) + 3 = 0$

$log^2_3 x - 4 log_3 x + 3 = 0$

Let log_3 x = w.

$w^2 - 4w + 3 = 0$

$(w - 3) (w - 1) = 0$

Hence, w = 3 or w = 1.

Substitute $log_3 x$ back.

$log_3 x = 3$ or $log_3 x = 1$

By definition, this means:

$x = 3^3 = 27$
or
$x = 3^1 = 3$

brightsky · « **Reply #6 on:** December 30, 2009, 07:49:54 pm »

b)

$log_3 x = log^2_3 x$

$log_3 x = (log_3 x) (log _3 x)$

$1 = \frac {(log_3 x) (log_3 x)} {(log_ 3x)}$

$1 = log_3 x$

By definition, this means:

$x = 3^1 = 3$

brightsky · « **Reply #7 on:** December 30, 2009, 07:55:50 pm »

c)

$\frac {(log_1_0 x)} {log_1_0 2} = 4$

$log_1_0 x = 4 log_1_0 2$

$log_1_0 x = log_1_0 2^4$

$log_1_0 x = log_1_0 16$

Hence, x = 16.

Aden · « **Reply #8 on:** December 30, 2009, 07:57:46 pm »

B)log3(x^3)=(log3(x))^2

$\log_3(x^3) = (\log_3(x))^2$
$3\log_3(x) = (\log_3(x))^2$
Let $\log_3(x)=y$
$y^2 - 3y = 0$
$y(y-3) =0$
$y= 0, 3$
$\log_3(x) = 0, 3$
$x = 3^0 , 3^3$
$x = 1, 27$

C)log3(x^2-3x-7)=1

$\log_3(x^2-3x-7) = 1$
$(x^2-3x-7) = 3^1$
$x^2-3x-10 = 0$
$x = -2, 5$

Please use LaTeX next time...

tolga · « **Reply #9 on:** December 30, 2009, 08:02:56 pm »

what is latex

brightsky · « **Reply #10 on:** December 30, 2009, 08:03:43 pm »

It's this:

$Latex!!!$

Edit: Just put [tex] at the start of every post.

And [tex] at the end, with a / in between the [ and the t.

tolga · « **Reply #11 on:** December 30, 2009, 08:07:55 pm »

what do you mean by a dash in between the [ and the t

brightsky · « **Reply #12 on:** December 30, 2009, 08:08:27 pm »

This [/tex].

tolga · « **Reply #13 on:** December 30, 2009, 08:10:07 pm »

what happens when we do that is that how the post appears and where can i get the mathematical equation symbols when posting a question

brightsky · « **Reply #14 on:** December 30, 2009, 08:12:08 pm »

It all becomes very confusing. (i.e. for fractions, you need to put \frac at the start and {} {} around your numerator and denominators), but yes, if you want to type maths, use latex. An easier option is for you to click on the TEX button, write under the Change Colour tab.

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