6.5 Logarithmic functions (in class)

Consider the logarithmic function [math]f(x)=e^{\ln x}[/math]. Which of the following functions is/are equivalent to [math]f(x)[/math]?

(Calculator) Let [math]f(x)=\log_2(x+5)[/math] with domain [math][0, 1000][/math]. How many integers [math]n[/math] such that [math]f(n)[/math] is also an integer?

(Calculator) Let [math]f(x)=\log_2(x^3+3x^2+7x+2)+1[/math]. If [math]g(x)=f^{-1}(x)[/math], how many intersections do [math]f(x)[/math] and [math]g(x)[/math] have?

Consider two functions [math]f(x)=\log_2(|x|)[/math] and [math]g(x)=|\log_2x|[/math]. Which of the following statements is/are true?

Let [math]a, b, c, d[/math] be real numbers satisfying [math]2^a=\log_{0.5}a, 0.5^b=\log_{0.5}b, \log_2c=0.5^c[/math], and [math]d=1[/math]. Order these numbers.