solve the following logarithmic equation. Be sure to reject any value of x that is not in thedomain of the orginal logarithmic expression. Give the exact answer.
log3(x+8)=4
The three actually drops down a little below the g. Can someone tell me how to do this?
since log3(x+8) = 4,
x+8 = 3^4
x+8 = 81
x = 73
To solve the logarithmic equation log3(x+8) = 4, we need to isolate x on one side of the equation.
Step 1: Convert from logarithmic form to exponential form.
In exponential form, the equation log3(x+8) = 4 can be written as 3^4 = x+8.
Step 2: Simplify the equation.
3^4 = 81, so the equation becomes 81 = x+8.
Step 3: Solve for x.
To isolate x, subtract 8 from both sides of the equation.
81 - 8 = x+8 - 8
73 = x
Therefore, the solution to the equation log3(x+8) = 4 is x = 73.
However, we also need to consider the domain of the original logarithmic expression log3(x+8). The argument of a logarithm must be positive, so x+8 > 0. Subtracting 8 from both sides, we have x > -8.
Therefore, the final solution is x = 73, while rejecting any value of x that is less than or equal to -8.