Using Log Graphs in Modelling (Edexcel A-Level Mathematics): Flashcards

Starts steep, less steep as $x$ increases, asymptote at $x=0$.

For $y = a^x$, the asymptote is at $y = 0$.

Shifts 3 units left; asymptote is $x = -3$.

Stretch by scale factor 2 parallel to $y$-axis.

No intersection; approaches zero asymptotically.

The y-intercept is $(0, 2)$. Since $2 \times 3^0 = 2$.

Set $2 \times 3^x = 8^x$ to find their intersection point.

Solve $x = (1/3)(3 - \log_{2}(3))$.

Base $10$ or natural logarithm (base $e$) are most common.

The curve falls exponentially as $x$ increases.