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^(2x)] = 4 Thank you all!! Bella 
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.

July 27th, 2014, 01:21 AM  #3 
Senior Member Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177  $\Large \color{blue}{3\cdot5^{2x}=4 \Longleftrightarrow\ 5^{2x} = \dfrac{4}{3}\ \Longleftrightarrow\ log_5 5^{2x} = log_5 \dfrac{4}{3}\ \Longleftrightarrow (2x)log_5 5 = log_5 \dfrac{4}{3} \Longleftrightarrow \\\;\\ \Longleftrightarrow\ 2x = log_5 \dfrac{4}{3}\ \Longleftrightarrow\ 2\log_5 \dfrac{4}{3} = x\ \Longleftrightarrow\ x = 2\log_5 \dfrac{4}{3} .}$ Last edited by aurel5; July 27th, 2014 at 01:24 AM. 
July 27th, 2014, 02:00 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
July 27th, 2014, 07:42 AM  #5 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  $\displaystyle 2x = \log_5 \frac{4}{3} \Rightarrow x = 2  \log_5 \frac{4}{3} = \log_5 25  \log_5 \frac{4}{3} = \log_5 \frac{25}{\frac{4}{3}}= \log_5 \frac{75}{4} = \log_5 18.75 \approx 1.82$

July 27th, 2014, 08:20 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  You forgot the expected ending: "in other words, 5^(~1.82) = 18.75" 
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.

July 27th, 2014, 09:29 AM  #8 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  
July 27th, 2014, 10:02 AM  #9  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
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! 

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