1. ## Logarithms & Differentiations help please

This is my first time on these forums tell me if im doing anything wrong! , thanks

First the Logarithms( Just learnt the latex functions lol had to read it before I posted)

Use the laws of logarithms to solve the following indicial equations:

(in each case check your answer by subtituting back the value for x)

5^(x+2)=8.5

6.5^x =8.4^(4x-10)

now for the Differential and integral calculus

Differentiate the following functions.

y=4x^3 -2x^2 + 5x^-3.7-6 w.r.t. x

s=4e^3t -e^-2.5t w.r.t. t

y=4sin2\theta-3cos4\theta w.r.t. \theta

Integrate the following expressions.

\int(2x^3-3x^2+5x-2)dx

\int (5sin2\theta+2cos4\theta)d\theta

This work has to be in by monday morning, im missing these questions and I have tons of other college work to get on with

2. Originally Posted by Problem_Solver11
This is my first time on these forums tell me if im doing anything wrong! , thanks

First the Logarithms( Just learnt the latex functions lol had to read it before I posted)

Use the laws of logarithms to solve the following indicial equations:

(in each case check your answer by subtituting back the value for x)

5^(x+2)=8.5

6.5^x =8.4^(4x-10)

now for the Differential and integral calculus

Differentiate the following functions.

y=4x^3 -2x^2 + 5x^-3.7-6 w.r.t. x

s=4e^3t -e^-2.5t w.r.t. t

y=4sin2\theta-3cos4\theta w.r.t. \theta

Integrate the following expressions.

\int(2x^3-3x^2+5x-2)dx

\int(5sin2\theta+2cos4\theta)d\theta

This work has to be in by monday morning, im missing these questions and I have tons of other college work to get on with,I will give the first person with all the answers and working out 20 pound through paypal to thank them, thanks alot.
For the first one take the natrual log of both sides. Then yank the exponent out as a coefficient and then solve for x.

For the differentiation ones

$\displaystyle \frac{d}{dx}\bigg[ax^n+bx^{n-1}+cx^{n-2}+\cdots\bigg]=\frac{d}{dx}\bigg[ax^n\bigg]+\frac{d}{dx}\bigg[bx^{n-1}\bigg]+\frac{d}{dx}\bigg[cx^{n-2}\bigg]+\cdots$

$\displaystyle \frac{d}{dx}\bigg[ax^n\bigg]=nax^{n-1}$

As for the other integrals, the concept of splitting works for integrals as well,

and finally

$\displaystyle \int{x^n}dx=\frac{x^{n+1}}{n+1}$

And $\displaystyle \int\sin(n\theta)d\theta=\frac{-\cos(n\theta)}{n}$

and

$\displaystyle \int\cos(n\theta)d\theta=\frac{\sin(n\theta)}{n}$

And don't forget $\displaystyle +C$, where $\displaystyle C$ is an abritrary constant of integration

3. I'm giving 30 pounds through paypal to people who don't do his homework for money.

Do you know that if $\displaystyle a^b = c$, then $\displaystyle b = \log_a c$ for values of $\displaystyle a,c>0~~~a\neq 1$?

Come on, I know you can do these if you want.

4. Originally Posted by wingless
I'm giving 30 pounds through paypal to people who don't do his homework for money.

Do you know that if $\displaystyle a^b = c$, then $\displaystyle b = \log_a c$ for values of $\displaystyle a,c>0~~~a\neq 1$?

Come on, I know you can do these if you want.
tamam ya habibi, btw mathstud are those the answers then :x?

5. Originally Posted by Problem_Solver11
tamam ya habibi, btw mathstud are those the answers then :x?
Not answers, tools to reach the answer. That is what you should truly be seeking.

6. Originally Posted by Mathstud28
Not answers, tools to reach the answer. That is what you should truly be seeking.
I really need the answers man it has to be in by monday otheriwise I might fail, i'm doing electronics engineering course and have to hand in alot on monday, but my teacher recently handed back my maths work and said 3 question were wrong and we did that ages ago and i've forgot how to do it, well to be honest I don't have time to do it, I would appreciate it alot.

7. Originally Posted by Problem_Solver11
I really need the answers man it has to be in by monday otheriwise I might fail, i'm doing electronics engineering course and have to hand in alot on monday, but my teacher recently handed back my maths work and said 3 question were wrong and we did that ages ago and i've forgot how to do it, well to be honest I don't have time to do it, I would appreciate it alot.
I will do the first one

$\displaystyle 5^{x+2}=8.5$

Taking the natural logs of both sides gives

$\displaystyle (x+2)\ln(5)=\ln(8.5)\Rightarrow{x=\frac{\ln(8.5)}{ \ln(5)}-2}$

I will also do one of each of the others

$\displaystyle \frac{d}{dx}\bigg[4x^3-2x^2+5x^{-3.7}-6\bigg]=12x^2-4x-18.5x^{-4.7}$

and

$\displaystyle \int\bigg[5\sin(2\theta)+2\cos(4\theta)\bigg]d\theta=\frac{-5}{2}\cos(2\theta)+\frac{1}{2}\sin(4\theta)+C$

8. Originally Posted by Mathstud28
I will do the first one

$\displaystyle 5^{x+2}=8.5$

Taking the natural logs of both sides gives

$\displaystyle (x+2)\ln(5)=\ln(8.5)\Rightarrow{x=\frac{\ln(8.5)}{ \ln(5)}-2}$
funny enough I have that one already I put it up to see if I was right, Thanks though