Question

Find please 4log4+5log5....

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Answer 1

Hey mate....

here's the answer....

= 4log4+5log5

= log 4⁴+log5^5

= log256+log3125

= log800000

= 5+ log8

Hope this helps♥

Answer 2

Answer:

$\boxed{\bf{\green{8+log5}}}$

Step-by-step explanation:

4 log 4 + 5 log 5

We know that n log b can be written as log bⁿ .

So 4 log 4 can be written as log 4⁴ .

Also 5 log 5 can be written as log 5⁵ .

⇒ log 4⁴ + log 5⁵ .

We also know that 4⁴ can be written as 4 × 4 × 4 × 4 = 256 .

So 5⁵ = 5 × 5 × 5 × 5 × 5 = 3125 .

⇒ log 256 + log 3125

We also know that by the properties of logarithm log a + log b can be written as log ab

⇒ log 256 + log 3125

⇒ log ( 256 × 3125 )

256 × 3125 = 800000

⇒ log ( 800000 )

⇒ log ( 8 × 10⁵ )

Now use the properties of log ab = log a + log b :

⇒ log 8 + log 10⁵

⇒ log 8 + 5 log 10

We know that log 10 = 1 and hence the above can be written as :

⇒ log 8 + 5 .

Thus the answer is $\boxed{\boxed{\bf{8+log5}}}$