Question

in the problem, $f(x)=\log_2 x$ and $g(x)=\log_{10} x$.
how are the graphs of $f$ and $g$ similar? choose two correct answers.
both increase from left to right.
both have an asymptote of $x=0$.
both have a y-intercept of 1
both have a domain of all real numbers.

Explanation:

1. For logarithmic functions $\log_b x$ where $b>1$:

• They are strictly increasing functions, so they rise left to right.
• The vertical asymptote is $x=0$ (since $x$ can never be 0 or negative, the graph approaches $x=0$ but never touches it).
• The domain is $x>0$, not all real numbers.
• The y-intercept would require $x=0$, which is undefined, so there is no y-intercept (the x-intercept is $x=1$, since $\log_b 1=0$).

Answer:

A. Both increase from left to right.
B. Both have an asymptote of $x = 0$.