Question

(-2/3)^6 × (4/9)^3 = (1/2)^3x
find the value of x​

Answer 1

Answer:

The value of x for the given algebric expression is 2.34

Step-by-step explanation:

Given as :

The algebric expression is

$(\dfrac{-2}{3})^{6}$  × $(\dfrac{4}{9})^{3}$ = $(\dfrac{1}{2})^{3x}$

Or, $(\dfrac{-2}{3})^{6}$  × $(\dfrac{2}{3})^{6}$ = $(\dfrac{1}{2})^{3x}$

Now, from the rule on indices

As base is same , so power is added

So, $(-1)^{6}$× $(\dfrac{2}{3})^{6}$ × $(\dfrac{2}{3})^{6}$ = $(\dfrac{1}{2})^{3x}$

or, 1 × $(\dfrac{2}{3})^{6+6}$ = $(\dfrac{1}{2})^{3x}$

Or, $(\frac{2}{3})^{12}$ = $(\dfrac{1}{2})^{3x}$

Taking Log with base 10 both side

Log  $(\frac{2}{3})^{12}$ = Log $(\dfrac{1}{2})^{3x}$

Or, 12 × Log $\dfrac{2}{3}$ = 3 x × Log $\dfrac{1}{2}$

Or, 12 × (- 0.176 ) = 3 x × (- 0.30)

Or, 2.112 = 0.9 x

∴   x = $\dfrac{2.112}{0.9}$

i.e x = 2.34

Hence, The value of x for the given algebric expression is 2.34 Answer