anonymous
  • anonymous
log base 4 (x^2-3) + log base 4 10= 1
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
log(base4) (x^2 - 3) + log(base 4) 10 = 1 addition of logs is the same as multiply so we can write it: log4(10*(x^2-3)) = 1 log4(10x^2 - 30) = 1 Write the exponent equiv of logs 4^1 = 10x^2 - 30 4 = 10x^2 - 30 4 + 30 = 10x^2 34 = 10x^2 x^2 = 34/10 x^2 = 3.4 x = underroot 3.4 x = 1.844 : 2) log(base 5)3 - log(base 5) 5x = 2 subtracting logs is the same as divide so we can write it log5(3/5x)2 exponent equiv 5^2 = 3/5x 25 = 3/5x Multiply by 5x 25(5x) = 3 125x = 3 x = 3/135
anonymous
  • anonymous
the answer is +/- square root 85/5 how do I get there?
anonymous
  • anonymous
product rule for logarithms \[\log_{a}x+\log_{a}y=\log_{a}xy\] \[\log_{4}[10(x^2-3)]=1\] convert to exponential notation \[4^1=10(x^2-3)\] \[10x^2-30=4\] \[10x^2-34=0\] \[5x^2-17=0\] Now you can apply the quadratic formula or complete the square to solve for x

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campbell_st
  • campbell_st
start with the left hand side \[\log _{4} (x^2 - 3) + \log _{4} 10 = \log _{4} (10(x^2 - 3))\] raising each term to be a power of 4 10x^2 - 30 = 4 10x^2 = 34 x^2 = 34/10 \[x = \pm \sqrt{34/10}\]
anonymous
  • anonymous
@ all my ans.. is correct
anonymous
  • anonymous
x = sqrt (3.4) = 1.84
anonymous
  • anonymous
the answer is +/- square root 85/5 how do I get there?
ash2326
  • ash2326
\[\log_4 (x^2-3)+ \log_4 (10)=1\] We know that \[\log_a b+ \log_a c=\log_a bc\] so using this here \[\log_4 (x^2-3) 10=1\] The most fundamental property of logarithms \[\log_a b=c=>b=a^c\] Using this we get \[(x^2-3) \times 10=4^1\] We get \[10x^2-30=4\] or \[10x^2=34\] \[x^2=\frac{34}{10}\] \[x^2=\frac{17}{5}\] Getting to your answer is quite easy Multiply numerator and denominator by 5 \[x^2=\frac{17 \times 5}{5 \times 5}\] We get \[x^2=\frac{85}{25}\] Take root both sides we get \[x=\pm \sqrt{\frac{85}{25}}\] we get finally \[x=\pm \frac{\sqrt{85}}{5}\]

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