# Logs :(

• December 10th 2012, 07:54 AM
Twinkie
Logs :(
Ok, I'm having some issues with these questions. So could you show me step by step on how to come to an answer.

1. write as a single logarithm in simplest form
(Log 16x^8)/4 - (Log 27x)/3

2. isolate x using laws of logarithims
3 Logx(4)=2
• December 10th 2012, 08:54 AM
topsquark
Re: Logs :(
Quote:

Originally Posted by Twinkie
1. write as a single logarithm in simplest form
(Log 16x^8)/4 - (Log 27x)/3

I'm afraid that I don't understand the final goal: "simplest form." So I'll show you how I would do the problem and you can make your own decision if the answer is simple enough.

We're going to be using the change of base formula:
$\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$

I'm going to choose my favorite base, e.

So
$\frac{1}{4}\log_{16}(x^8) - \frac{1}{3} \log_{27}(x)$

Skipping a couple of steps, you should arrive at
$2 \left [ \frac{ln(x)}{ln(16)} \right ] - \frac{1}{3} \left [ \frac{ln(x)}{ln(27)} \right ]$

Which has the final form, as simply as I can write it:
$\left [ \frac{1}{2~ln(2)} - \frac{1}{9~ln(3)} \right ] ln(x)$

The only other thing I can think of would be to subtract the fractions.

-Dan
• December 10th 2012, 08:57 AM
topsquark
Re: Logs :(
Quote:

Originally Posted by Twinkie
2. isolate x using laws of logarithims
3 Logx(4)=2

$\log_x(4) = 2$

$x^{\log_x(4)} = x^2$

$4 = x^2$

And you can finish from there. Watch out for the extra (wrong) solution that comes from this.

-Dan
• December 10th 2012, 09:14 AM
Twinkie
Re: Logs :(
Ok thankyou for your help. :)
• December 10th 2012, 01:44 PM
bjhopper
Re: Logs :(
1. log 16x^8/4 - log27x/3
2.log4x^8 - log 9x
3.log4x^8/9x
4.log 4/9x^7
• December 10th 2012, 05:15 PM
Twinkie
Re: Logs :(
That kind of question makes sence now, but I have anouther question that I'm not sure how to do.
Solve.
3log(6) X= log(6) 9+ log(6) 24
• December 10th 2012, 05:31 PM
topsquark
Re: Logs :(
Quote:

Originally Posted by bjhopper
1. log 16x^8/4 - log27x/3
2.log4x^8 - log 9x

The division of 4 in the first term is outside the logarithm. So you can't divide through.

-Dan
• December 10th 2012, 05:36 PM
topsquark
Re: Logs :(
Quote:

Originally Posted by Twinkie
That kind of question makes sence now, but I have anouther question that I'm not sure how to do.
Solve.
3log(6) X= log(6) 9+ log(6) 24

If the bases on all the logs are the same then we can do this rather easily. Let's get everything to one side:
$2\log_6(x) - \log_6(9) - \log_6(24) = 0$

Let's rewrite that first term:
$\log_6(x^2) - \log_6(9) - \log_6(24) = 0$

Now we can use
$\log_a(p) + \log_a(q) = \log_a(pq)$

and
$\log_a(p) - \log_a(q) = \log_a \left ( \frac{p}{q} \right )$

(Note: These are only true when the base a is the same on all log functions.)

Can you finish from here?

-Dan
• December 10th 2012, 06:36 PM
bjhopper
Re: Logs :(
Quote:

Originally Posted by Twinkie
That kind of question makes sence now, but I have anouther question that I'm not sure how to do.
Solve.
3log(6) X= log(6) 9+ log(6) 24

Twinkie,
1.log base 6 (x)^3= log b6 (9*24) =log b6 (216)
2. x^3 = 216
3. x=6
• December 10th 2012, 07:22 PM
bjhopper
Re: Logs :(
Quote:

Originally Posted by topsquark
The division of 4 in the first term is outside the logarithm. So you can't divide through.

-Dan

Dan, That was a mistake but when I redo the question I come up with log 2/3 X^5/3 as the simplified log
• December 11th 2012, 08:34 AM
Twinkie
Re: Logs :(
Ok thanks! :)
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7251139879226685, "perplexity": 3110.1349609421286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246658116.80/warc/CC-MAIN-20150417045738-00230-ip-10-235-10-82.ec2.internal.warc.gz"}