
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 2nd, 2014, 04:10 PM  #1 
Newbie Joined: Oct 2014 From: Canada Posts: 7 Thanks: 0  Need Help Please.. Really Confused!!
I am having trouble completing these following homework questions and I would like to learn how to do them soon as I have a midterm exam coming up in 2 days. Any help will be really appreciated. Thanks 1) Express in exponential or logarithmic form, whichever isn't given. 1a) y=27(1/3)^2x 1b) 3log_5(z)x^2=2x+1 2) Express the following as a single logarithm expression in the most simplified form: log(x)^1/2+3log(z)[log(z)^4+5log(x square rooted by 3) 5) Solve for x. 5c) 2(27)^x=9^(x+1) 6) The halflife of Co60 is 15.83 years. Determine how long it takes for 3.5mg of Co60 to decay to 1mg. Round your answer to two decimals places. 7) In a particular circuit, the current, I, in amperes, can be found using the formula I(t)=1.2511.251(10^0.02668t), after t seconds. 7a) What is the current in the circuit after 1 minute? 7b) Rewrite the equation for I(t), solving for t. 7c) Use the equation in part b to determine the time it takes for the current to reach 0.5A. 10) Solve log_5x+log_25x+log_125x=33. Any help would be really appreciated. If anyone who helps could please explain the steps of what they did to get the answer, that would be really useful for me to learn how to do the questions. Please just don't give the final answer as my main goal is learn the process of how to do the questions. Thanks again. Last edited by skipjack; November 2nd, 2014 at 05:43 PM. 
November 2nd, 2014, 05:49 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,113 Thanks: 2327 
Can you post your attempts? By the way, the halflife of Co60 is nothing like 15.83 years (5.27 years would be about right). 
November 2nd, 2014, 07:15 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, Confusion9! Here is some help . . . Quote:
$\qquad\quad =\;\log\left(x^{\frac{1}{2}}\cdot x^{\frac{5}{3}}\right) + \log\left(\frac{1}{z}\right) \;=\; \log\left(x^{\frac{13}{6}}\right) + \log\left(\frac{1}{z}\right)$ $\qquad\quad=\;\log\left(x^{\frac{13}{6}}\cdot \frac{1}{z}\right) \;=\;\log\left(\frac{x^{\frac{13}{6}}}{z}\right)$ Quote:
$\quad 2(3^{3x})  3^{2x+2} \:=\:0 \quad\Rightarrow\quad 3^{2x}\left(2\cdot3^x  3^2\right) \:=\:0$ Hence: $\:3^{2x} \:=\:0$ . . . not possible $\quad$ and: $\:2\cdot 3^x 9 \:=\:0 \quad\Rightarrow\quad 3^x \,=\,\frac{9}{2}$ Take logs: $\:\ln(3^x) \:=\:\ln\left(\frac{9}{2}\right) \quad\Rightarrow\quad x\ln 3 \:=\:\ln\left(\frac{9}{2}\right) $ Therefore: $\:x \:=\:\dfrac{\ln(\frac{9}{2})}{\ln3}$ Quote:
$\log_5x \:=\:\dfrac{\ln x}{\ln 5}$ $\log_{25}x \:=\:\dfrac{\ln x}{\ln25} \:=\:\dfrac{\ln x}{\ln(5^2)} \:=\:\dfrac{\ln x}{2\ln 5}$ $\log_{125}x \:=\:\dfrac{\ln x}{\ln125} \:=\:\dfrac{\ln x}{\ln(5^3)} \:=\:\dfrac{\ln x}{3\ln 5}$ The equation becomes: $\displaystyle\:\frac{\ln x}{\ln 5} + \frac{\ln x}{2\ln 5} + \frac{\ln x}{3\ln 5} \:=\:33$ $\displaystyle\qquad \frac{6\ln x}{6\ln 5} + \frac{3\ln x}{6\ln 5} + \frac{2\ln x}{6\ln 5} \:=\:33 \quad\Rightarrow\quad 6\ln x + 3\ln x + 2\ln x \:=\:33\!\cdot\!6\ln 5$ $\qquad 11\ln x \:=\:198\ln 5 \quad\Rightarrow\quad \ln x \:=\:18\ln 5$ $\qquad \ln x \:=\:\ln\left(5^{18}\right) \quad\Rightarrow\quad x \:=\:5^{18}$ Last edited by skipjack; November 2nd, 2014 at 07:56 PM.  
November 2nd, 2014, 07:48 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,113 Thanks: 2327 
(5c). $\displaystyle 2(27)^x=9^{x+1} \implies \log_3(2) + \log_3(27)x = \log_3(9)(x + 1) \\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \implies \log_3(2) + 3x = 2(x + 1) = 2x + 2$ (10). $\displaystyle 33*6 = 6\log_5(x) + 3\log_5(x) + 2\log_5(x) = 11\log_5(x),\text{ so }\log_5(x) = 18.$ 

Tags 
confused, have an exam soon, homework help, please help 
Search tags for this page 
express as a single logarithm. simplify, if possible. ${log}_{\frac{1}{3}} 27 {log}_{\frac{1}{3}}\frac{1}{9}$,what is the simplified form of the expression \frac{4 {\frac{1}{2}}\cdot{37}}{3}?,"1.251×10" years how long
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help!! A.s.a.p. I'm really confused!  Josh  Algebra  2  November 13th, 2013 02:38 PM 
Confused  Shamieh  Calculus  3  September 7th, 2013 05:27 PM 
Confused with the Three  SarahW  Algebra  1  May 14th, 2013 01:50 PM 
Confused  Ballser  Academic Guidance  60  January 14th, 2012 06:23 PM 
So confused with this  charlieboon  Algebra  0  December 31st, 1969 04:00 PM 