A basic equation for a base ten logarithmic plot is y = l o g 10 ( x) which can be rearranged to 10 y = x What this means is that for every one value of y, the value of x will increase by a factor of ten, and vice versa. Using a logarithmic scale
This equation simplifies by taking u / p to be a new variable, u / p = q. Then u = pq, so that du = q dp + p dq. The equation then becomes which simplifies to which split into partial fractions
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How To: Given a logarithmic equation, use a graphing calculator to approximate solutions Press [Y=]. Enter the given logarithmic equation or equations as Y1= and, if needed, Y2=. Press [GRAPH] to observe the graphs of the curves and