log(2x)=4
log2x=4 in exponential form using the definition of a logarithm. If
x x and b b are positive real numbers and b ≠ 1, then log b(x)=y logbx=y is equivalent to by=x. 10 4 = 2x
hope it helps
Answer and explanation:
Given : The transformation(s) that take place on the parent function [tex]f(x) = \log(x)[/tex] to achieve the graph of [tex]g(x) = \log(-3x-6) - 2[/tex].
To find : Describe the transformation(s) ?
Solution :
Parent function [tex]f(x) = \log(x)[/tex]
1) Translate the graph of function to horizontally compress
i.e. f(x)→f(ax), a>0
So, [tex]f(x) = \log(3x)[/tex] i.e. horizontally compress with 3 units.
2) Translate the graph of function to the left with a unit
i.e. f(x)→f(x+a)
So, [tex]f(x) = \log(3x+6)[/tex] i.e. Horizontal shift left with 6 units.
3) Translate the graph of function to the down with b unit
i.e. f(x)→f(x)-b
So, [tex]f(x) = \log(3x+6)-2[/tex] i.e. Vertical shift down with 2 units.
4) Translate the graph of function by reflection about the y-axis
i.e. f(x)→f(-x)
So, [tex]f(x) = \log(-3x-6)-2[/tex] i.e. Reflection about the y-axis.
