Mathematical Process Standards>Analyzing Mathematical Relationships to Connect Ideas(TEKS.P.9-12.1.F) Practice Test

Multiplying inside the logarithm causes a vertical stretch of the exponential by the same factor.

They are inverses: graphs reflect across $y=x$, domains and ranges swap, and the horizontal asymptote $y=0$ for $a^x$ corresponds to the vertical asymptote $x=0$ for $\log_a x$.

Logarithms are the derivatives of exponentials of the same base, so their slopes match at corresponding points.

They share the same horizontal asymptote $y=0$ and both pass through $(0,1)$.