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Alex787 [66]
2 years ago
13

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

Mathematics
1 answer:
Sloan [31]1 year ago
5 0

Answer:

1. a = 1

2. See explanation below.

Step-by-step explanation:

<u>First Question</u>

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}

__________________________________________________________

<u>Second Question</u>

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.

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