Question

2 log 18 + 3 log 24 - 6 log 6 =​

Answer 1

Answer:

1.98227123304

Step-by-step explanation:

Answer 2

Answer:

The value of the expression 2log18 + 3log24 - 6log6 is $1.982$

Step-by-step explanation:

Recall the rules of logarithm,

(i) log$a$ + log$b$ = log($ab$)

(ii) log$a$ - log$b$ = log($\frac{a}{b}$)

(iii) $a$log$b$ = log$b^a$

Consider the given expression as follows:

2log18 + 3log24 - 6log6

Rewrite as follows:

2log$(2\times 3^2)$ + 3log$(2^3\times 3)$ - 6log$(2\times3)$

Using rule of logarithm (i), we have

⇒ 2(log2 + log$3^2$) + 3(log$2^3$ + log3) - 6(log2 + 6log3)

⇒ 2log2 + 2log$3^2$ + 3log$2^3$ + 3log3 - 6log2 - 6log3

Simplify as follows:

⇒ (2log2 - 6log2) + (3log3 - 6log3) + 2log$3^2$ + 3log$2^3$

⇒ - 4log2 - 3log3 + 2log9 + 3log8

Now, using rule of logarithm (iii), we get

⇒ - log$16$ - log$27$ + log$81$ + log$512$

Rearrange the expression as follows:

⇒ (log$81$ - log$27$) + (log$512$ - log$16$)

Using rule of logarithm (i), we get

⇒ log$(\frac{81}{27} )$ + log$(\frac{512}{16} )$

⇒ log3 + log32

Since log3 = 0.477 and log 32 = 1.505

Substituting the values, we get

⇒ 0.477 + 1.505

⇒ 1.982

Therefore, the value is $1.982$.