Question

If the log↓b(a)=0, what is the value of a?explain why log↓0 (3) and log↓1 (3) do not exist. ​

Answer 1

Answer:

1. a = 1

2. See explanation below.

Step-by-step explanation:

First Question

Given:

$\displaystyle \large{\log_b a = 0}$

Convert to exponential:

$\displaystyle \large{\log_b a = c \to b^c = a}$

Thus $\displaystyle \large{\log_b a = 0 \to b^0 = a}$

Evaluate:

$\displaystyle \large{b^0 = a}$

We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.

Solution:

$\displaystyle \large{a = 1}$

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Second Question

Given:

$\displaystyle \large{log_0 3}$ and $\displaystyle \large{\log_1 3}$

Let’s convert to an equation:

$\displaystyle \large{\log_0 3 = x}$ and $\displaystyle \large{\log_1 3 = y}$

The variables represent unknown values of logarithm.

Convert to exponential:

$\displaystyle \large{0^x = 3}$ and $\displaystyle \large{1^y = 3}$

Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.

Hence, no solutions for x and y.