My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
Reply
 
LinkBack Thread Tools Display Modes
July 26th, 2014, 09:18 PM   #1
Newbie
 
Joined: Jul 2014
From: Seattle

Posts: 16
Thanks: 0

Exponent

How would I go about solving the following problem:

[3 x 5^(2-x)] = 4


Thank you all!!

Bella
bml1105 is offline  
 
July 26th, 2014, 09:28 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,674
Thanks: 2654

Math Focus: Mainly analysis and algebra
You will need to take logarithms to get the $x$ out of the exponent.
v8archie is offline  
July 27th, 2014, 01:21 AM   #3
Senior Member
 
aurel5's Avatar
 
Joined: Apr 2014
From: Europa

Posts: 584
Thanks: 177

Quote:
Originally Posted by bml1105 View Post

[3 x 5^(2-x)] = 4

$\Large \color{blue}{3\cdot5^{2-x}=4 \Longleftrightarrow\ 5^{2-x} = \dfrac{4}{3}\ \Longleftrightarrow\ log_5 5^{2-x} = log_5 \dfrac{4}{3}\ \Longleftrightarrow (2-x)log_5 5 = log_5 \dfrac{4}{3} \Longleftrightarrow
\\\;\\
\Longleftrightarrow\ 2-x = log_5 \dfrac{4}{3}\ \Longleftrightarrow\ 2-\log_5 \dfrac{4}{3} = x\ \Longleftrightarrow\ x = 2-\log_5 \dfrac{4}{3} .}$

Last edited by aurel5; July 27th, 2014 at 01:24 AM.
aurel5 is offline  
July 27th, 2014, 02:00 AM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by bml1105 View Post
[3 x 5^(2-x)] = 4
Please use * as multiplication sign:
3 * 5^(2-x) = 4

Rule: if x^p = y, then p = LOG(y) / LOG(x)
So (divide by 3):
5^(2-x) = 4/3
2 - x = LOG(4/3) / LOG(5)
Finish it...
Thanks from topsquark
Denis is offline  
July 27th, 2014, 07:42 AM   #5
Senior Member
 
tahirimanov's Avatar
 
Joined: Nov 2013
From: Baku

Posts: 502
Thanks: 56

Math Focus: Geometry
Quote:
Originally Posted by Denis View Post
Please use * as multiplication sign:
3 * 5^(2-x) = 4

Rule: if x^p = y, then p = LOG(y) / LOG(x)
So (divide by 3):
5^(2-x) = 4/3
2 - x = LOG(4/3) / LOG(5)
Finish it...
$\displaystyle 2-x = \log_5 \frac{4}{3} \Rightarrow x = 2 - \log_5 \frac{4}{3} = \log_5 25 - \log_5 \frac{4}{3} = \log_5 \frac{25}{\frac{4}{3}}= \log_5 \frac{75}{4} = \log_5 18.75 \approx 1.82$
tahirimanov is offline  
July 27th, 2014, 08:20 AM   #6
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by tahirimanov View Post
$\displaystyle 2-x = \log_5 \frac{4}{3} \Rightarrow x = 2 - \log_5 \frac{4}{3} = \log_5 25 - \log_5 \frac{4}{3} = \log_5 \frac{25}{\frac{4}{3}}= \log_5 \frac{75}{4} = \log_5 18.75 \approx 1.82$
You forgot the expected ending: "in other words, 5^(~1.82) = 18.75"
Denis is offline  
July 27th, 2014, 09:11 AM   #7
Newbie
 
Joined: Jul 2014
From: Seattle

Posts: 16
Thanks: 0

Thanks everyone! I'll be sure to use a * sign next time.
bml1105 is offline  
July 27th, 2014, 09:29 AM   #8
Senior Member
 
tahirimanov's Avatar
 
Joined: Nov 2013
From: Baku

Posts: 502
Thanks: 56

Math Focus: Geometry
Quote:
Originally Posted by Denis View Post
You forgot the expected ending: "in other words, 5^(~1.82) = 18.75"
I like unexpected endings....
tahirimanov is offline  
July 27th, 2014, 10:02 AM   #9
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,257
Thanks: 928

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by aurel5 View Post
$\Large \color{blue}{3\cdot5^{2-x}=4 \Longleftrightarrow\ 5^{2-x} = \dfrac{4}{3}\ \Longleftrightarrow\ log_5 5^{2-x} = log_5 \dfrac{4}{3}\ \Longleftrightarrow (2-x)log_5 5 = log_5 \dfrac{4}{3} \Longleftrightarrow
\\\;\\
\Longleftrightarrow\ 2-x = log_5 \dfrac{4}{3}\ \Longleftrightarrow\ 2-\log_5 \dfrac{4}{3} = x\ \Longleftrightarrow\ x = 2-\log_5 \dfrac{4}{3} .}$
What? No poetry?

-Dan
topsquark is offline  
July 27th, 2014, 11:17 AM   #10
Newbie
 
Joined: Jul 2014
From: Seattle

Posts: 16
Thanks: 0

Can anyone tell me how to make the subscripts for the log formulas when writing on the forum?

Thanks!
bml1105 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
exponent



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Exponent Thinkhigh Calculus 3 March 2nd, 2012 06:42 AM
Exponent Laws happysmiles374 Elementary Math 2 February 28th, 2012 08:48 AM
variable and the exponent skarface Algebra 1 January 24th, 2010 03:28 PM
Complex exponent greg1313 Applied Math 3 November 17th, 2009 07:39 PM
Mudulo exponent alfonso1 Number Theory 17 August 7th, 2007 09:03 AM





Copyright © 2019 My Math Forum. All rights reserved.