Hi i don't know how to do this problem
solve for n^3
given that log(40 SQRT(3))/log(4n) = log(45)/log(3n)
Thanks i'm copletely lost and don't know how to solve
let a=log(40 sqrt(3)) and b=log45
then
a/log(4n)=b/log(3n)
a(log3n)=b*log(4n)
a(log3+logn)=b(log4+logn)
logn(a-b)=blog4-alog3
logn=( )/(a-b)
logn^3=3logn= 3*above
then take the antilog of both sides, it looks like fun.
hmmm
how did you go from this
a(log3+logn)=b(log4+logn)
to this?
logn(a-b)=blog4-alog3
logn=( )/(a-b)
You are supposed to fill in the blanks.
alog3+alogn=blon4=blogn
logn(a-b)=blog4-alog3
logn= (blog4-alog3)/(a-b)
well if follow now but don't know how to take the anti log of that mumbo jumbo
n = 10^(3((blog4-alog3)/(a-b) )
im unsure how that simplifies
To solve for n^3 in the given equation, we need to isolate the term involving n.
Let's proceed step by step:
Step 1: Simplify the equation
First, let's simplify both sides of the equation using logarithmic properties.
Using the property log(a)/log(b) = log(base b)a,
the given equation becomes:
log(40√3) / log(4n) = log(45) / log(3n)
Next, use the quotient rule of logarithms to combine the fractions:
log(40√3 * log(3n) )/ (log(4n))
Step 2: Convert from logarithmic to exponential form
Now, let's convert the logarithmic equation to an exponential equation. In exponential form, log(base b)(a) = c is equivalent to b^c = a.
Using this property, we can rewrite the equation as:
40√3 * log(3n) = (4n)^(log(45)/log(3n))
Step 3: Solve for n
To solve for n, we need to isolate the n term on one side of the equation. Let's simplify the right side first:
(4n)^(log(45)/log(3n)) = (4n)^(log(45) * (1 / log(3n)))
Using the property (a^b)^c = a^(b * c), we simplify further:
(4n)^(log(45) * (1 / log(3n))) = (4n)^((log(45) / log(3n))
Now, rewrite the equation as an exponential equation:
40√3 * log(3n) = (4n)^(log(45) / log(3n))
Step 4: Further simplification
To simplify further, we need to rewrite the term (4n)^(log(45) / log(3n)).
Using the property (a^b)^c = a^(b * c), we have:
(4n)^(log(45) / log(3n)) = (4n)^(log(45) * (1 / log(3n)))
Now, we can rewrite the equation as:
40√3 * log(3n) = (4n)^(log(45) / log(3n))
Step 5: Solving for n
At this point, we have simplified the equation, but it is not possible to directly solve for n algebraically. We can use numerical methods or approximations to find the value of n^3.
One approach would be to use a graphing calculator or software to plot the functions y = 40√3 * log(3n) and y = (4n)^(log(45) / log(3n)), and find the point(s) of intersection. The x-coordinate(s) of the intersection point(s) would correspond to the possible value(s) of n.
Alternatively, you can use iterative numerical methods such as Newton's method or the bisection method to approximate the value of n that satisfies the equation.
Please note that the exact solution to this equation may be difficult to obtain without additional information or assumptions.