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 May 12th, 2019, 05:56 AM #1 Member   Joined: Nov 2016 From: USA Posts: 36 Thanks: 1 Change of Base - please verify Two part question: Use Change of Base to show how to calculate log base 4 (62). Then find its equivalent in log base 2. Round answers to nearest thousandth. I attempted both parts. Please check my math strategies. Thank you. PART ONE (log 62)/(log4) =(1.79239)/(0.6020599) =2.977 PART TWO: find equivalent in log base 2 log2 (N) = 2.977 2^2.977 = N N=7.873 Is this a correct method to solve? Thank you. May 12th, 2019, 03:51 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 $x=\log_4(62) \implies 4^x=62 \implies (2^2)^x = 62 \implies 2^{2x} = 62 \implies 2x =\log_2(62) \implies x = \dfrac{1}{2} \log_2(62) = \log(62)^{1/2} = \log_2 \sqrt{62}$ $\sqrt{62} \approx 7.874$ Thanks from Seventy7 May 12th, 2019, 05:12 PM #3 Member   Joined: Nov 2016 From: USA Posts: 36 Thanks: 1 Thank you. I'm going to post little more detail from your steps to quickly clarify for myself if I reference this post again in future: 4^x=62 (2^2)^x=62 (2)^2x=62 b^P=N log base b (N) = Power so the (2)^2x=62 becomes log base 2 (62)=2x divide both sides by 2 [log base 2 (62)]/2 = 2x/2 0.5 log base 2 (62) = x use logarithm property power rule: log base b (M^p) = p log base b (M) rewrite as: log base 2 (62^0.5) = x 62^0.5 is sqrt 62 log base 2 (sqrt 62) ---------------------------- Another method using Change of Base formula to log base 2: log base 4 (62) = 2.977098155 log (x) / log 2 = 2.977098155 log (x) / 0.3010299957 = 2.977098155 Then cross multiply the decimal and 2.977098155 log base 10 (x) = 0.89616958447 10^0.89616958447 =7.874 May 12th, 2019, 05:46 PM   #4
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Quote:
 Originally Posted by Seventy7 find its equivalent in log base 2.
That wording is unclear.

I think it's intended to mean "find log$_{_{\large2}}\!$(62)", which is 5.954 to 3 decimal places. Tags base, change, verify Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post chakana Computer Science 2 June 19th, 2015 09:14 PM caters Number Theory 9 May 22nd, 2014 02:46 AM Jhenrique Algebra 2 November 10th, 2013 02:45 AM bilano99 Algebra 3 October 11th, 2012 08:10 AM momesana Algebra 4 December 3rd, 2009 06:13 PM

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