My Math Forum Change of Base - please verify

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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.

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