What is the value of x?

(1/3)^x-2 =(1/3)^2

Step-by-step explanation:

Hi there,

To solve this, we want to isolate x either using logs or exponent rules. For this, I chose exponent rules.

First, divide both sides of the equation by (1/3)² :

The right-hand side is reduced to 1. The left-hand side contains values that have the same base, so we can use this exponent rule:

Apply this:

    Now, we are left with:

Conceptually, you just have to think: what exponent can make a base equal to 1?

This is based on the following exponent rule:

So, all we have to do is set (x-4) = 0!

Thus, the value of x is 4.

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x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1