3^x=9x

please show workings

this kind of problem is hard to solve in general. But, list the first few powers and multiples of 3, and it should not take long to find the answer.

yeah, but diz theory qstn. You mean it can't be solved?? what abt using theory of logarithm?

well, ok. I spoke to soon. Of course, if you know about logs, then

3^x = 9x
x log3 = log9 + logx
xlog3 - logx = log9

Unfortunately, that isn't any easier to solve than the original equation.

To solve the equation 3^x = 9x, we need to find the value(s) of x that satisfy the equation. Here's how we can do that:

Step 1: Start by taking the logarithm (base 3) of both sides of the equation. This will help us eliminate the exponent and convert the equation into a form that we can solve more easily. We can use the logarithm property that states if log base a of b equals c, then a raised to the power of c equals b. Applying this property, we have:

log base 3 (3^x) = log base 3 (9x)

Since log base a of a raised to the power of b equals b, the left side simplifies to:

x = log base 3 (9x)

Step 2: Now, let's simplify the right side of the equation. We can use the logarithm property that states log base a of b^c equals c times log base a of b. Applying this property, we have:

x = log base 3 (9) + log base 3 (x)

Step 3: Continue simplifying by evaluating the logarithms. The logarithm of 9 with base 3 is equivalent to x + 1, and the logarithm of x with base 3 remains as it is:

x = x + 1 + log base 3 (x)

Step 4: Next, isolate the log base 3 (x) term on one side of the equation:

x - log base 3 (x) = x + 1

Step 5: Subtract x from both sides:

- log base 3 (x) = 1

Step 6: Multiply both sides by -1 to isolate the logarithm:

log base 3 (x) = -1

Step 7: Finally, exponentiate both sides of the equation with base 3:

3^log base 3 (x) = 3^-1

x = 1/3

So, the solution to the equation 3^x = 9x is x = 1/3.