plz plz solve it with explanation

muhammadalihamid · #1 Saturday, October 16, 2010

23. If 2x. 2y = 3z, x+y/z=?

A. 1.330
B. 1.750
C. 0.750
D. 1.585
E. 1.425

x,y or z yaha powers ma hn copy kia ha is lia asa ho gia ha

j87ibz · #2 Saturday, October 16, 2010

So this is question.
2^x .2^y=3^z

simplify the LHS of equation by the combining factors which have same bases.

2^(x+y)=3^z

Take log to both sides of equation,

log{2^(x+y)}= log {3^z}

by property of logs,

x+y(log2) =z( log 3)

where log3 =0.4771
and log 2= 0.3010

Put in the above equation,we get

x+y(0.3010) = z(0.4771)

divide the equation by z,and divide by 0.3010 both sides we get,

(x+y)/ z = 0.4771/ 0.3010 => 1.5859

muhammadalihamid · #3 Saturday, October 16, 2010

thanx but in the test calculator is not allowed so any other method to solve without log.plz

j87ibz · #4 Saturday, October 16, 2010

Usually they provide constant values in test,I think they must have given it
or they may have assumed values of log2 or log3 within scope of the attempter.

certainly there are other methods,but they are lengthy and may be beyond the scope of 1 mark objective.

for example : through power series of exponents

Just like e^x = 1+ x + (x^2/2!) + ..........

but that is very very complex.......

or by taking Integral to both sides of the given equation,but it will involve three functions and chain rule on LHS........so very difficult.

bear · #5 Sunday, October 17, 2010

1.6 is closest to 1.5858

always use this method to solve logs if you dont have calculator

FOR EXAMPLE
log 2 can separately be calculated as

2^ 10 = 1024
10^3 = 1000
2^ 10 ~= 10^3
hence ,
10 * log 2 ~= 3 * log 10
10 * log 2 ~= 3 * 1
log 2 ~= 3 /10
log 2 ~= 0.3

see attached image for above post

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The Following User Says Thank You to j87ibz For This Useful Post:
Mehria (Saturday, October 16, 2010)