SOLUTION: if (125/27)^x = the cubic root of 0.6 then the value of x is _______
Algebra.Com
Question 202363: if (125/27)^x = the cubic root of 0.6 then the value of x is _______
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your original equation is:
by the laws of logarithms, this can only be true if and only if
we can convert this log with a base of (125/27) to a log with a base of 10 so that we can solve it using the calculator.
the logarithm base conversion formula is:
our formula now becomes:
= x.
-----
now:
is the same as .
also:
is the same as
so the equation becomes:
x = /
you can now use your calculator to solve this.
the equation becomes:
x =
which becomes:
x =
which becomes:
x = -0.1111111111111
-----
to prove your answer is correct, substitute it in the original equation to get:
this becomes:
which is true.
note that .843432665 = (.6)^(1/3)
-----
RELATED QUESTIONS
if x>1 and square root of a over x cubic equals x^m what is the value of... (answered by Tatiana_Stebko)
If f(x)= 3(1/125)(^x-2)+12,then what is the value of x when... (answered by bucky)
If one root of the equation x^2-px+20=0 is four, while the equation x^2-qx+20=0 has equal (answered by ikleyn)
: If one root of the equation x^2-px+20=0 is four, while the equation x^2-qx+p=0 has... (answered by ikleyn)
If one root of the equation x^2-px+20=0 is four while the equation x^2-qx+p=0 has equal... (answered by greenestamps,ikleyn)
If the equations x^2+2x-3=0 & x^2+3x-k=0 have a comman root then the non-zero value of k... (answered by sachi)
If y = 32.56x + 27 and x = 0, what is the value of... (answered by longjonsilver)
What is the value of 3 square root... (answered by stanbon)
what is the value of x in the equation ?
(square root 5x)-12=13
a. 1/125
b. 1/5... (answered by JBarnum)