Question

Can anyone help with this?

Answer 1

The logarithmic function expresses the output variable, y, as a function of the logarithm of the input variable, x, as a function of a base b. The true statements are therefore;

• I, II, and III only

Which statements are true based on the definition of a logarithm?

The given logarithmic equation is presented as follows;

$y = log_{b}(x)$

Therefore, we have;

$x = {b}^{y}$

Where b = 1, we have that x will always be 1, therefore;

• b ≠ 1
• Option III is true

$b = \sqrt[y]{x}$

Therefore;

• x > 0
• Option I is true

Which gives;

• b > 0
• Option II is true

The statements that are true is therefore;

• I, II, and III only

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