Julik
Julik Julik
  • 24-07-2015
  • Mathematics
contestada

[tex]5^{1+log_4x}+5^{log_{0.25}x-1}=\frac{26}{5}[/tex]

Respuesta :

CarlosMath
CarlosMath CarlosMath
  • 24-07-2015
[tex]\displaystyle 5^{1+\log_4 x}+5^{-\log_4x-1} = \frac{26}{5}\\ \\ \text{Sea } z=5^{1+\log_4 x} \text{ entonces}: \\ \\ z+\frac{1}{z}=\frac{26}{5}\\ \\ 5z^2-26z+5=0 \\ \\ (5z-1)(z-5)=0 \\ \\ z\in\left\{\frac{1}{5};5\right\}\\ \\ \text{Then: }\\ \\ 5^{1+\log_4x}=5^{-1} \vee 5^{1+\log_4x}=5\\ \\ 1+\log_4x=-1 \vee 1+\log_4x=1\\ \\ \log_4x =-2 \vee \log_4x=0 \\ \\ x=\frac{1}{16} \vee x=1\\ \\ \text{Answer: }x\in\left\{\frac{1}{16};1\right\} [/tex]
Answer Link

Otras preguntas

The force between two charged objects is equal to 400 N. What will be the force between the two objects if the charge on both objects is doubled?​
Help me with this im confused
Complete the sentence. A(n) ___ interface is one that supports as many people as possible by considering disabilities, screen sizes, languages, and many other f
100 POINTS!!!!!!! please help me with this question.
help please fast .. this is in the class
Which statement best describes how the author develops the idea that newspapers may report the same story much differently? 1. By detailing various examples of
Why is africa's life expectancy so low 80 words
An automobile traveled 320 miles in 6 hours. What is its average speed?
Japan also has a/an Dictator President Queen Emperor
classify 8x³-9x the polynominal by its degree and number of term