Question

find the value of x​

Answer 1

Answer:

Basic Rules used in this problem:

→ logₐ(a) = 1

→ logₐ(x/y) = logₐ(x) - logₐ(y)

→ logₐ(xⁿ) = n × logₐ(x)

Given:

$\implies log_{5}\:(\dfrac{4\sqrt{25}}{625})$

$\implies log_5\: ( \dfrac{25^{1/4}}{625})\\\\\\\text{Using Rule No. 2 we get:}\\\\\\\implies log_5\: (25)^{1/4} - log_5\: 625\\\\\\\implies log_5\: (5^2)^{1/4} - log_5\:(5)^4\\\\\\\text{Using Rule No. 3, we get:}\\\\\\\implies \dfrac{2}{4}\times log_5\:(5) - 4 \times log_5\:(5)\\\\\\\text{ Using Rule No. 1 we get:}\\\\\\\implies \dfrac{2}{4} \times 1 - 4 \times 1\\\\\\\implies \dfrac{1}{2} - 4 \:\: \implies \dfrac{ 1-8}{4}\\\\\\\implies \boxed{\dfrac{-7}{4}}$

Hence x = (-7/4)

Answer 2

Answer:

Answer:

Basic Rules used in this problem:

→ logₐ(a) = 1

→ logₐ(x/y) = logₐ(x) - logₐ(y)

→ logₐ(xⁿ) = n × logₐ(x)

Given:

\implies log_{5}\:(\dfrac{4\sqrt{25}}{625})⟹log

5

(

625

4

25

)

\begin{gathered}\implies log_5\: ( \dfrac{25^{1/4}}{625})\\\\\\\text{Using Rule No. 2 we get:}\\\\\\\implies log_5\: (25)^{1/4} - log_5\: 625\\\\\\\implies log_5\: (5^2)^{1/4} - log_5\:(5)^4\\\\\\\text{Using Rule No. 3, we get:}\\\\\\\implies \dfrac{2}{4}\times log_5\:(5) - 4 \times log_5\:(5)\\\\\\\text{ Using Rule No. 1 we get:}\\\\\\\implies \dfrac{2}{4} \times 1 - 4 \times 1\\\\\\\implies \dfrac{1}{2} - 4 \:\: \implies \dfrac{ 1-8}{4}\\\\\\\implies \boxed{\dfrac{-7}{4}}\end{gathered}

⟹log

5

(

625

25

1/4

)

Using Rule No. 2 we get:

⟹log

5

(25)

1/4

−log

5

625

⟹log

5

(5

2

)

1/4

−log

5

(5)

4

Using Rule No. 3, we get:

⟹

4

2

×log

5

(5)−4×log

5

(5)

Using Rule No. 1 we get:

⟹

4

2

×1−4×1

⟹

2

1

−4⟹

4

1−8

⟹

4

−7

Hence x = (-7/4)

Step-by-step explanation:

mark as BRAINLEST ANSWER please please please