Find the solution or solutions of the equation:
3^x=3/2x+6
Thank You ;)
To find the solution or solutions of the equation 3^x = 3/2x + 6, we can start by simplifying the equation as much as possible.
Let's rearrange the equation and rewrite it in a more manageable form:
3^x = (3/2)x + 6
Now, we want to get rid of the fractional exponent. To do this, we can take the logarithm of both sides of the equation. Let's choose the natural logarithm, denoted as ln:
ln(3^x) = ln((3/2)x + 6)
Using the properties of logarithms, we can bring the exponent down in front:
x * ln(3) = ln((3/2)x + 6)
Now, we want to isolate x. Divide both sides of the equation by ln(3):
x = ln((3/2)x + 6) / ln(3)
This gives us an expression for x in terms of itself, so we'll need to use numerical methods or an approximation technique to find the solution. One method to find an approximate solution is using iterative methods like Newton's method.
Alternatively, you could use a graphing calculator or a computer algebra system to solve the equation by graphing both sides and finding the intersection point(s).