Solve the function
2(9^x) - 5(3^×) = 12
So what I did So far is changed it into log functions:
2(9^x) = 12
9^x = 6
Log9(6) = x
And then
5(3^x) = 12
3^x = 12/5
Log3(12/5) = x
So then I don't know how to subtract them because they have different bases :/
who are you and why are you using my name?
... my name's also rose? I'm just trying to get math help man
kay
2*(3^2)^x - 5*3^x = 12
2*3^x *3^x - 5*3^x = 12
let z = 3^x
2 z^2 -5 z -12 = 0
z = 4 or -3/2
so
3^x = 4
or
3^x = -1.5
now x log 3 = log 4 etc
To solve the equation 2(9^x) - 5(3^x) = 12, you're on the right track by converting it into logarithmic form. However, in order to subtract the logarithms with different bases, you need to convert them to the same base first.
Let's start with the first equation: 2(9^x) = 12. To convert it into logarithmic form, you would take the logarithm of both sides of the equation using a base that will help eliminate the exponent on the 9. Since 9 can be expressed as 3^2, we can use logarithm base 3:
Log3(2(9^x)) = Log3(12)
Using the exponent rule for logarithms, we can bring the exponent down as a coefficient:
x * Log3(9) = Log3(12/2)
Simplifying further, Log3(9) is equal to 2:
x * 2 = Log3(12/2)
x = Log3(6)
Now let's move on to the second equation: 5(3^x) = 12. Similarly, we can convert it into logarithmic form using logarithm base 3:
Log3(5(3^x)) = Log3(12)
Again, using the exponent rule for logarithms, we can bring the exponent down as a coefficient:
x * Log3(3) = Log3(12/5)
Log3(3) is equal to 1, so:
x = Log3(12/5)
Now you have two separate expressions for x, Log3(6) and Log3(12/5). Unfortunately, you cannot directly subtract them because they have different bases.
To solve this, you can use the change of base formula for logarithms, which states that log base a of b can be expressed as log base c of b divided by log base c of a. In other words:
Logc(b) = Loga(b) / Loga(c)
Applying this formula, divide both expressions by Log3(3):
x = (Log3(6)) / (Log3(3))
x = (Log3(12/5)) / (Log3(3))
Now that both expressions have the same base, you can subtract the logarithms:
x = (Log3(6) - Log3(3))
x = (Log3(12/5) - Log3(3))
Compute the logarithms and subtract them to find the value of x.
Note: If you are unable to compute logarithms directly, you can use a calculator or an online tool that supports logarithmic operations.