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1. The given equation is presented as follows;

The above equation can be rewritten as follows;

...(1)

Therefore, taking logarithm to base 3 of both sides of the equation, the above equation can be rewritten without an exponent as follows;

...(2)

2. Inverse relationship of exponents is given as follows;

(1/a)ˣ = a⁻ˣ

Therefore, we have;

1/9 = 1/(3²) = (3²)⁻¹ = 3⁻²

Taking log of both sides of gives;

From logarithm rules, we have;

From equation (2), we have;

Therefore, the equation can be simplified by dividing both sides by the common factor, , as follows;

Therefore, we get;

2·x - 1 = -2...(3)

3. Solving 2·x - 1 = -2, gives;

2·x - 1 = -2

2·x = -2 + 1 = -1

x = -1/2 = -0.5

x = -0.5

EQUATION 3

The given equation is presented as follows;

1. By the property of exponents, we have;

125 = 5³

Therefore, we get;

2. Given that we can rewrite the given equation as follows;

Therefore;

Both sides of the equation are given in powers of 5, therefore, the appropriate base logarithm to use on both sides to rewrite the equation is logarithm to base 5

3. Using logarithm, by applying logarithm to both sides, we get;

Dividing both sides by log₅5 gives;

∴ 3 × x - 3 = x

3 × x - x = 3

2·x = 3

x = 3/2 = 1.5

x = 1.5

Step-by-step explanation:

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