given that f(x)=11^x, find x when f(x)=7
a) x=Ln(7/11)
b) x=Ln7/Ln11
c) x= 7/11
d) x= ll sub 7 11
so you solving:
11^x = 7
take ln of both sides
ln(11^x) = ln7
x(ln11) = ln7
x = ln7/ln11
To find the value of x when f(x) = 7, you can set up the equation f(x) = 7 and solve for x.
Given that f(x) = 11^x, we have:
11^x = 7
To determine the correct option among the provided answer choices, let's analyze each one:
a) x = Ln(7/11)
This option uses the natural logarithm (Ln). However, it does not represent the correct solution in this case.
b) x = Ln7/Ln11
This option uses the logarithmic property that states Ln(a^b) = b * Ln(a). In this case, we have the equation Ln(11^x) = x * Ln(11), which is not equivalent to our original equation. Thus, this is not the correct solution either.
c) x = 7/11
This option suggests that the value of x is 7 divided by 11. However, this is not accurate, as it does not correspond to solving the exponential equation.
d) x = ll sub 7 11
This option seems to contain a typographical error and is not interpretable. Therefore, it cannot be considered.
Since none of the provided options is correct, we need to find another approach to solve the equation.
To solve 11^x = 7, we can take the logarithm of both sides using any logarithmic base. Let's use the natural logarithm (Ln) here:
Ln(11^x) = Ln(7)
Applying the logarithmic identity Ln(a^b) = b * Ln(a), we have:
x * Ln(11) = Ln(7)
Now, we can solve for x:
x = Ln(7) / Ln(11)
Therefore, the correct answer is:
x = Ln(7) / Ln(11)