Question

10/3 * 3^x -3^(x-1) = 81Solve for x.​

Answer 1

Answer:

$\boxed{ \rm \: x = 3}$

Step-by-step explanation:

Equation given:

10/3 × 3^x -3^(x-1) = 81

Finding the value of x :

$\implies \rm \: \cfrac{10}{3} \times 3 {}^{x} - \cfrac{3 {}^{x} }{3} = 81$

• (We took 3^x-1 as 3^x/3 because according law x^m-n = x^m/x^n)

$\implies \rm \cfrac{10 \times 3 {}^{x} }{3} - \cfrac{3 {}^{x} }{3} = 81$

$\implies \rm \cfrac{10 \times 3 {}^{x} - 3 {}^{x} }{3} = 81$

Taking 3x common,we get:

$\implies \rm \cfrac{3 {}^{x}(10 - 1) }{3} = 81$

$\implies \rm3 {}^{x} \times \cfrac{ \cancel9}{ \cancel{3} } = 81$

$\implies \rm3 {}^{x} \times 3 = 81$

$\implies \rm {3}^{x} = \cfrac{ \cancel{81} \: {}^{27} }{ \cancel3}$

$\implies \rm3 {}^{x} = 3 {}^{3}$

Since according to the law of exponents,if the bases are equal then the powers are equal too.

$\implies \rm{x} = \boxed3$

Hence,the value of x is 3.

Answer 2

Answer:

$x=3$

Step-by-step explanation:

$~~~~~~~\dfrac{10}{3} \cdot 3^x - 3^{x-1} = 81\\\\\\\implies 10 \cdot 3^{x-1} - 3^{x-1} = 81~~~~~~~~~~~~~~~~~~~~;\left[\dfrac{a^m}{a^n} =a^{m-n} \right]\\\\\\\implies 9\cdot 3^{x-1} = 81\\\\\\\implies 3^{x-1} = \dfrac{81}{9}\\\\\\\implies 3^{x-1} = 9\\\\\\\implies 3^{x-1} = 3^2\\\\\\\implies x -1 = 2\\\\\\\implies x = 2+1\\\\\\\implies x = 3$