Question 574198
{{{F(x) =log( 2, (x+1))-3}}}
b) F(x) = -1
Substitute the given value for F(x):
{{{-1 =log( 2, (x+1))-3}}}
Now solve for x.<br>
To solve for x in an equation like this we usually start by transforming the equation into one of the following forms:
log(expression) = other_expression
or
log(expression) = log(other_expression)<br>
Since your equation has only a single log in it, we will aim for the first form. All we have to do to add three to each side:
{{{2 =log( 2, (x+1))}}}<br>
With the equation in the first form, then next step is to rewrite the equation in exponential form. In general, {{{log(a, (p)) = q}}} is equivalent to {{{a^q = p}}}. Using this pattern on your equation we get:
{{{2^2 = x+1}}}
which simplifies to:
4 = x + 1<br>
With the logarithm now gone the equation is simple to solve, Just subtract 1 from each side:
3 = x<br>
When solving equations like
{{{-1 =log( 2, (x+1))-3}}}
it is important, <i>not optional</i>, to check your answer! You have to ensure that all arguments (and bases) remain valid (i.e. positive). Checking x = 3:
{{{-1 =log( 2, (3+1))-3}}}
We can quickly see that the only log's argument is 4. And its base is 2. These are both valid/allowable numbers so the required part of the check is complete.<br>
So F(3) = -1 which means the point (3, -1) is a point on the graph of F(x).<br>
c) Find the zeros. This just means find the x value or values where the function's value is zero. IOW: Find all x's such that F(x) = 0. Solve this just like part b (using 0, instead of -1 of course).