Question

Find the value of x if (-3)3x+1 × (-3)4 = (-3)8​

Answer 1

Take 3^x common from both 3^(x-1) and 3^(x+1) as the first step. After that solve the equation.

Here I shall use a basic concept of Index ::--

if a^x = a^m [ a≠1 ] then x=m [ where x is a variable and m is a real number ]

If a=1 , then x may or may not equal to m .

NOW,

3^(x-1) + 3^(x+1) = 90 , [ taking 3^x common ]

=> (⅓ + 3) • 3^x = 90 ,

=> 10/3 • 3^x = 90 ,

=> 3^x = 90 • 3/10 = 270/10 = 27 ,

=> 3^x = 3³

=> x=3 [ from the basic concept of index mentioned above ]

So the value of x is 3 .

PLS THANKED ME

Answer 2

x = $1 \frac{1}{3 \\ }$

GIVEN:- (-3)3x+1 × (-3)4 = (-3)8

TO FIND:- Value of x

SOLUTION:-

• In mathematics, brackets indicate multiplication.
• When a negative number is multiplied by a positive number then the product is a negative number.

According to the question, RHS is equal to LHS, so we need to find the value of x by evaluating the brackets.

$(-3)3x+1 × (-3)4 = (-3)8 \\ - 9x + 1 \times ( - 12) = - 24 \\ - 9x - 12 = - 24$

When we shift a number or a variable from one side to another then the sign changes

$- 12 + 24 = 9x \\ 9x = 24 - 12 \\ 9x = 12 \\ x = \frac{12}{9} \\ x = \frac{4}{3} \\ x = 1 \frac{1}{3}$

Hence, x = $1 \frac{1}{3 \\ }$

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