Question

what is A×B×C
pls display the answer with solution ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{ABC=log_{6}(4)}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies A= log_{32}(1024) \\ \\ \tt: \implies B= log_{81}( \sqrt{3} ) \\ \\ \tt: \implies C = log_{6}(256) \\ \\ \red{\underline \bold{to \: find:}} \\ \tt: \implies ABC = ?$

• According to given question :

$\tt: \implies A = log_{32}(1024) \\ \\ \tt: \implies A= log_{32} ({32})^{2} \\ \\ \tt: \implies A= 2 \: log_{32}(32) \\ \\ \green{\tt: \implies A= 2} \\ \\ \bold{For \: B : } \\ \tt: \implies B = log_{81}( \sqrt{3} ) \\ \\ \tt: \implies B = log_{( \sqrt{3})^{8} }( \sqrt{3} ) \\ \\ \tt: \implies B= \frac{1}{8} log_{ \sqrt{3} }( \sqrt{3} ) \\ \\ \green{\tt: \implies B = \frac{1}{8}} \\ \\ \bold{For \: C: } \\ \tt: \implies C = log_{6}(256) \\ \\ \tt: \implies C = log_{(2 \times 3)}( {2}^{8} ) \\ \\ \tt: \implies C = 8 \: log_{2 \times 3}(2) \\ \\ \green{\tt: \implies C=8 \: log_{6}(2) } \\ \\ \bold{For \: finding \: value} \\ \tt: \implies ABC = 2 \times \frac{1}{8} \times 8 \: log_{6}(2) \\ \\ \tt: \implies ABC=2 \: log_{6}(2) \\ \\ \green{\tt: \implies ABC = log_{6}(4) }$

Answer 2

Answer:

Given:

• A = log₃₂ (1024)

• B = log₈₁ (√3)

• C = log₆ (256)

Find:

• A × B × C = ?

According to the question:

Finding value of A:

⇒ A = log₃₂ (1024)

⇒ A = log₃₂ (32)²

⇒ A = log₃₂ (32)

⇒ A = 2

Finding value of B:

⇒ B = log₈₁ (√3)

⇒ B = log(√₃)⁸ (√3)

⇒ B = log₈₁ (√3)

⇒ B = log(√₃)⁸ (√3)

⇒ B = 1/2 log √₃ (√3)

⇒ B = 1/8

Finding value of C:

⇒ C = log₆ (256)

⇒ C = log(₂ × ₃) (2)⁸

⇒C = log(₂ × ₃) (2)

⇒C = log₆ (2)

Finding the values:

⇒ A × B × C = 2 × 1/2 × 8 log₆ (2)

⇒ A × B × C = 2 log₆ (2)

⇒ A × B × C = log₆ (4)

Therefore, The value of A × B × C = log₆ (4).