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3 years ago

Please help me answer this.

Mathematics

1 answer:

adoni [48]3 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

Statements Reasons

1. $\overline{AD}\parallel \overline{BC}$ Given

2. $\angle ADB\cong \angle CBD$ As alternate interior angles when parallel lines AD and BC intersect by ltransversal BD

3. $\overline{AD}\cong \overline{BC}$ Given

4. $\overline{BD}\cong \overline{DB}$ Reflexive property

5. $\triangle ADB\cong \triangle CBD$ SAS postulate

6. $\angle ABD\cong \angle CDB$ Corresponding parts of congruent triangles are congruent

7. $\overline{AB}\parallel \overline{CD}$ Inverse alternate interior angles theorem

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Answer:

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Anvisha [2.4K]

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Which equation is equivalent to log subscript 3 baseline (x 5) = 2? 3 squared = left-bracket log subscript 3 baseline (x 5) righ

wolverine [178]

The equation that is equivalent to the considered equation of log is given by: Option E: 2^3 = x+5

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get $a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = \log_a(c)$

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

$\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)$

Log with base e = 2.71828... is written as $\ln(x)$ simply.

Log with base 10 is written as $\log(x)$ simply.

The equation given is:

$\log_3(x+5) = 2$

By using the definition of log, which says $a^b = c \leftrightarrow \log_a(c) = b$ , we get:

$(x+5) = 2^3$ or $2^3 = x+5$

Thus, the equation that is equivalent to the considered equation of log is given by: Option E: $2^3 = x+5$

(we used the fact that the question is asked in a way that expresses that there is only one equivalent equation. Plus we used the fact that as option E is a sure equivalent version, so it is correct option).

Thus, the equation that is equivalent to the considered equation of log is given by: Option E: $2^3 = x+5$

Learn more about logarithm here:

brainly.com/question/20835449

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