Answer to Question #132154 in Algebra for DIDI

Question

Write your explanations to the right of each step as you would explain the following
algebraic problem to a learner:
2.3x=162
3x= 81
3x=34
x = 4

Answer 1

We are given $2.3^x = 162$

The equation can be written clearly as $2(3^x) = 162$

Step 1:

Divide both sides of the equation by 2 to reduce it.

$=> \dfrac {2(3^x)}{2} = \dfrac {162}{2}$

$=> 3^x = 81$

Step 2:

Write 81 to base 3 such that the expressions on both the L.H.S and R.H.S are raised to the same base, 3.

$=> 3^x = 3^4$

Step 3:

Equate powers since both the L.H.S and the L.H.S of the equation are raised to the same base.

$Note: \space a^m = a^n => m = n$

$\therefore \space 3^x = 3^4 => x = 4$

Step 4:

Conclude,

$If \space 2.3^x = 162 , \space \space Then \space x= 4$