Answers:
(a) x = 0.5
(b) Given Below.
Explanation:
(a)
[tex]4^x = 2[/tex]
apply ln both sides
[tex]ln(4^x) = ln(2)[/tex]
simplify
[tex]xln(4) = ln(2)[/tex]
divide both sides by ln(4)
[tex]x = 0.5[/tex]
(b)
Recall that rational numbers can be expressed in fractions a/b
[tex]4^x = 5[/tex]
apply ln on both sides
[tex]ln( 4^x) = ln(5)[/tex]
simplify
[tex]xln( 4) = ln(5)[/tex]
divide both sides by ln(4)
[tex]x =\frac{ ln(5)}{ln(4)}[/tex]
simplify
[tex]x =1.160964047...[/tex] The value is endless and continues.
The following cannot be expressed as a fraction or whole number.
Hence, the following value of x is irrational.
