# Thread:

1. ## Answer Checks!!

ok so i did these problems and i would like someone to check my answers and telll me how i did...thanks alot

find an exact solution for each problem.

4x+19=e^(2ln(x))

so i rearanged this equation to

x^2-4x-19=0

then from there i used the quadratic eq. and came up with

x= 2+sqrt(23) and x=2-sqrt(23)

next one

1-2sin(t)/ln(t)=0

rearranged this to get

1-2sin(t)=0

then

sin(t)=1/2

i did inverse sin of 1/2 and came up with pi/6
the problem wanted the exact solution for

2pi<t<5pi/2

and with that i came up with 13pi/6

and for the last one

f(x)=4^x, and the slope of the tangent line of f(x) at x=0 is
f`(x)=ln4. use the tangent line to estimate f(0.11) and f(0.2)

i used ln4 for m is the equation

y=mx+b

then plugged one of the given points in 4^x to get a y value, then used the x and y to find b in the tangent line equation, once i found b i plugged in the given values to find y

i came up with

f(0.11) = 1.14

f(0.2) = 1.28

if someone could check my answers and let me know how i did that would be great thanks alot

mathlete

2. mathlete, mathlete, mathlete... I expect more from you.

Rule #1 -- It's not an equation if you don't see one of these "=".

Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

After requiring x > 0, how do you feel about your answers?

3. yes i know its not an equation without an = sign...

i meant to put

x^2-4x-19=0

sorry

Originally Posted by TKHunny
mathlete, mathlete, mathlete... I expect more from you.

Rule #1 -- It's not an equation if you don't see one of these "=".

Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

After requiring x > 0, how do you feel about your answers?

4. You didn't address the Domain Issues.

5. Ok, well tell me what was wrong with the equation that i rearranged

Originally Posted by TKHunny
You didn't address the Domain Issues.

6. Already did. See Rule #2, Above.

$e^{2ln(x)}$ is not quite $x^{2}$. What's the difference?

Note: If we allow x to be complex, and the logarithm to provide complex values, then maybe they are EXACTLY the same. I still don't like it, but I guess I can deal with my emotional issues. :-)
{"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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "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": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9539802074432373, "perplexity_flag": "middle"}