solve for x.
485 * 5^x+2 = 12^2x-1
take the ln of each side
ln485+(x+2)ln5=(2x-1)ln12
look up the ln of the above, then gather terms, solve for x.
is ln the same as log?
and is its ln485 + or ln485 * ?
ln(ab)= ln a + ln b
To solve this equation for x, we need to simplify both sides of the equation and then isolate the variable x.
Let's start by simplifying the equation:
485 * 5^(x + 2) = 12^(2x - 1)
We can rewrite 12^(2x - 1) as (12^2)^(x - 1) since the exponent can be distributed.
485 * 5^(x + 2) = (12^2)^(x - 1)
Now, let's simplify further:
485 * 5^(x + 2) = 144^(x - 1)
Next, we need to rewrite 144 as a power of 12 because we know that 12^2 = 144.
485 * 5^(x + 2) = (12^2)^(x - 1)
485 * 5^(x + 2) = (12^2)^((x - 1)(1))
Using the rule (a^b)^c = a^(b*c), we can rewrite the right side of the equation as:
485 * 5^(x + 2) = 12^((2)(x - 1))
Now, let's simplify further:
485 * 5^(x + 2) = 12^(2x - 2)
Now, both sides of the equation have the same base (12), so we can equate the exponents:
x + 2 = 2x - 2
Next, let's isolate the variable x by subtracting x from both sides and adding 2 to both sides:
x - 2x = -2 - 2
Simplifying further, we have:
- x = -4
Finally, divide both sides by -1 to solve for x:
x = 4
Therefore, the solution to the equation is x = 4.