Question

I need someone who would know how to convert a log to a base of 10? I'll post the question and what work I have done in the comments :)

Answer 1

The computer system you need to input the function into only works in logarithms of base 10. Using complete sentences, explain how to convert your exponential function P(x) in a logarithmic one and then into a base 10 logarithm.

Log10 / log2 --> (1) / (0.301) = 3.321 not sure if this is correct or not but the equation I used was P(x) = 2^2 --> log_2 4 = 2

Answer 2

What is your exponential function? Can you give me the problem as it is in your book or whatever?

Answer 3

Yes hold on :)

Answer 4

Months
(x) Population
P(x)
0 2
1 4
2 16
3 256

x^2 = P(x)

Answer 5

This is what I did and numbers I plugged in @IMStuck

Answer 6

will have to come back to you; my family needs me to cook dinner now! But I'll be back in a bit! Promise!

Answer 7

Oh okay :( Well thanks and I hope to get help when you get back :)

Answer 8

\(\Large \begin{array}{llll}
x\qquad &y
\\\hline\\
{\color{brown}{ 0}}&2\to 2^1\to 2^{2^{\color{brown}{ 0}}}\\
{\color{brown}{ 1}}&4\to 2^2\to 2^{2^{\color{brown}{ 1}}}\\
{\color{brown}{ 2}}&16\to 2^4\to 2^{2^{\color{brown}{ 2}}}\\
{\color{brown}{ 3}}&256\to 2^8\to 2^{2^{\color{brown}{ 3}}}
\end{array}\)

Answer 9

Are those logs? That confused me a little sorry :(

Answer 10

ahemm... no, just p(x), meaning that \(\huge \bf p(x)= 2^{2^{\color{brown}{ x}}}\)

Answer 11

so is that my equation? Sorry that makes no sense to me I'm completely confused :S

Answer 12

heehhe

Answer 13

well, you're trying to get a logarithmic equation from the dataset provided, right?

Answer 14

I have no clue how to get a log out of that so would you mind helping me find it?

Answer 15

\(\Large \bf recall\implies {\color{red}{ a}}^y={\color{blue}{ b}}\implies log_{\color{red}{ a}}{\color{blue}{ b}}=y\)

Answer 16

so log_2 4 = 2 is my log ?

Answer 17

well \(\bf recall\implies {\color{red}{ a}}^y={\color{blue}{ b}}\implies log_{\color{red}{ a}}{\color{blue}{ b}}=y
\\ \quad \\
{\color{blue}{ p(x)}}={\color{red}{ 2}}^{2^x}\implies log_{{\color{red}{ 2}}}{\color{blue}{ p(x)}}=2^x\)

Answer 18

how do I change the base to 10?

Answer 19

use the "change of base rule", that is \(\bf \textit{log change of base rule }log_{\color{red}{ a}}{\color{blue}{ b}}\implies \cfrac{log_{\color{olive}{ c}}{\color{blue}{ b}}}{log_{\color{olive}{ c}}{\color{red}{ a}}}\qquad thus
\\ \quad \\

log_2[p(x)]=2^x\implies \cfrac{log_{{\color{olive}{ 10}}}[p(x)]}{log_{{\color{olive}{ 10}}}2}=2^x\)

Answer 20

for the log change of base rule, the log base can be any number, so long it's the same above and below

Answer 21

in this case we just happen to use base 10