# How do you graph y = log _4 (x) - 3?

May 27, 2016

The graph of y vs log x on a semi-log graph paper will be a straight line with slope $\frac{1}{\log} 4$. with y-interceot = $- 3$.

#### Explanation:

Use log_4 x= log x/log 4.

Here, $y = {\log}_{4} x - 3 = \log \frac{x}{\log} 4 - 3$.

y is a linear function of X = log x..

If X-graduation is in the logarithmic scale

( 1 for log 10, 2 for log 100, ..., n for $\log {10}^{n}$),

the graph paper is semi-logarithmic.

On this graph paper, the graph for the given equation will be a

straight line, with $\frac{1}{\log} 4 = 1.661$, nearly, with y-intercept $= - 3$.