# Sum of the Values of X, Exponential Equation

by wiraimperia
Tags: equation, exponential, logarithm, sum, values
 P: 9 1. The problem statement, all variables and given/known data (4x)^(1 + log(base 2) (x)) = 8(x^3) What is the sum of the values of x that fullfill that equation? A) 2.5 B) 2.0 C) 1.5 D) 1.0 E) 0.5 2. Relevant equations Use the exponential equation only and make the lower one (exponented) 1. 3. The attempt at a solution (4x) = (2 x^(1/2))^2 8(x^3) = (2x)^3 If I insert x = (1/4) to make 4x = 1 it doesn't fulfill the equation.. So does x = (1/2).. I cannot simplify the exponential equation... Any assistance please?
 PF Patron HW Helper Sci Advisor Thanks P: 25,486 hi wiraimperia! (try using the X2 and X2 buttons just above the Reply box ) for any number n, what is nlog2(x) ?
 HW Helper Sci Advisor Thanks P: 9,060 $$4x(4x)^{\log_2x} = 8x^3$$ ... how many values of x satisfy the equation? I'd recheck for x=1/2 ...
P: 9

## Sum of the Values of X, Exponential Equation

I mean if it has 2 solutions, then we are asked X1 + X2, if it has 3, then X1 + X2 + X3, and so on...
HW Helper
Thanks
P: 9,264
 Quote by wiraimperia I cannot simplify the exponential equation... Any assistance please?
Try to take the logarithm of both sides.

ehild
 PF Patron HW Helper Sci Advisor Thanks P: 25,486 for any number m, what is (2m)log2(x) ?
HW Helper
 P: 3,050 Taking logarithm on both sides with base 2, you get: $$(1+log_2 x)log_2(4x)=3+3log_2 x$$ It is easy to solve now.