Question

(root 3/root 5)^x+1=125/27 find x

Answer 1

Answer:

Step-by-step explanation:

root3/root5 can also be written as

(3/5)^1/2

now

(3/5)^(1/2×x+1)=125/27

(3/5)^(x+1)/2=(5/3)^3

=(3/5)^-3

(x+1)/2=-3

x+1=-3×2

x+1=-6

x=-6-1=-7

Answer 2

Concept:

Root of a number is when that number is multiplied by itself given how many times the numbers are multiplied to itself. If a number is multiplied 2 times by itself then it is called square of that number and if the number is multiplied  times then it is called cube of that number and so on.

A number's square root is a value that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Squares and square roots are hence linked ideas.

Given information:

The following mentioned equation is given:

$(\frac{\sqrt{3} }{\sqrt{5} } )^{x+1}=\frac{125}{27}$

To find:

Find the value of x in the given equation.

Solution:

$(\frac{\sqrt{3} }{\sqrt{5} } )^{x+1}=\frac{125}{27}$

$(\frac{\sqrt{3} }{\sqrt{5} } )^{x+1}=(\frac{\sqrt{3} }{\sqrt{5} } )^{-6}$

Bases are same so we can equate the powers of the function.

$x+1=-6$

     $x=-7$

Hence, the value of x is $-7$.

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