Question

find the Value of x for which (5/3) to the power -4×(5/3) to the power-5=(5/3) to the power 3x​

Answer 1

add -4 + -5 = 3x

so 3x = -9

x= -3

Answer 2

The value of x is -3.

Step-by-step explanation:

Given : Expression $(\frac{5}{3})^{-4}\times (\frac{5}{3})^{-5}=(\frac{5}{3})^{3x}$

To find : The value of x ?

Solution :

$(\frac{5}{3})^{-4}\times (\frac{5}{3})^{-5}=(\frac{5}{3})^{3x}$

Using exponent rule, $a^b\times a^c=a^{b+c}$

$(\frac{5}{3})^{-4+(-5)}=(\frac{5}{3})^{3x}$

$(\frac{5}{3})^{-4-5}=(\frac{5}{3})^{3x}$

$(\frac{5}{3})^{-9}=(\frac{5}{3})^{3x}$

Compare the base,

$-9=3x$

$x=-\frac{9}{3}$

$x=-3$

Therefore, the value of x is -3.

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