1. ## Logarithmic problem

Hi,

Can someone please tell me how to solve the attached logarithmic problem ? the answer should be 5.
Attached is also my working.

Thanks

2. ## Re: Logarithmic problem

log(x^2-5)-log(x) = log(4)

Use the logarithmic law that states that log(a)-log(b) = log(a/b)

(x^2-5)/x = 4
x^2-5 = 4x

Solving this equation gives the solution x = -1 and x = 5.

But since negative solutions are not defined in the equation log(x) the only solution is x = 5.

3. ## Re: Logarithmic problem

the original equation was ...

$\displaystyle \log\left(\frac{x^2-5}{x}\right) = \log{4}$

not ...

$\displaystyle \log(x^2-5) - \log{x} = \log{4}$

why can't $\displaystyle x = -1$ ?

4. ## Re: Logarithmic problem

Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.

Another problem. The result of the attached problem is 6.66 while on the book it states that the result should be 6.058. What am I doing wrong? Isn't it gust (Ln14.91/(Ln1.5) ??

5. ## Re: Logarithmic problem

Originally Posted by aritech
Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.

Another problem. The result of the attached problem is 6.66 while on the book it states that the result should be 6.058. What am I doing wrong? Isn't it gust (Ln14.91/(Ln1.5) ??
i would just take ^1/1.5 on both side on that problem :P

6. ## Re: Logarithmic problem

Originally Posted by aritech
Thanks for the reply. At skeeter, no the first one was the is the original equation. There is another attachment.
ok ... now I see it.

7. ## Re: Logarithmic problem

Hi,

Can someone tell me how to work the binomial attached??

the answer should be 34749 p^8q^5

8. ## Re: Logarithmic problem

your binomial coefficient is incomplete ...

$\displaystyle \binom{13}{8} \cdot (3p)^8 \left(\frac{q}{3}\right)^5$

$\displaystyle \frac{13!}{8!(13-8)!} \cdot (3^3 p^8 q^5)$

$\displaystyle 34749p^8q^5$

... next time, start a new problem with a new post. Do not piggy-back onto an older one.

9. ## Re: Logarithmic problem

From where did you bring the 13/8 ??

Attached is the full question and working:

10. ## Re: Logarithmic problem

Originally Posted by aritech
From where did you bring the 13/8 ??

Attached is the full question and working: