Question

Find the value of: log base 3 × log base 5 × log base 3^243​

Answer 1

The value of log₃log₅log₃ (243​) is 0.

Given:

log₃log₅log₃ (243​)

To Find:

The value of log₃log₅log₃ (243​).

Solution:

We have,

log₃log₅log₃ (243​) → [1]

We know,

243 = 3⁵ → [2]

Putting the value of [2] in [1],

we have,

log₃log₅log₃ (243​)

= log₃log₅log₃ 3⁵

we know, log mⁿ = n × log m

i.e,

log₃log₅ × 5 × log₃ 3

Again,

we know, that if the log has the same base and answer, then the argument is always equal to 1. i.e, logₓX = 1

Therefore,

log₃log₅ × 5 × log₃ 3

= log₃log₅ × 5 × 1

= log₃log₅ × 5

= log₃log₅ 5 [Also, log₅ 5 = 1]

= log₃ 1

And we know, that log 1 being any base it be, is equal to zero.

So,

log₃ 1 = 0

Thus, the value of log₃log₅log₃ (243​) is 0.

#SPJ1

Answer 2

The value of log$_{3}$ log$_{5}$ log$_{3}$ 243 is 0.

Given,

log$_{3}$ log$_{5}$ log$_{3}$ 243

To Find,

The value of log$_{3}$ log$_{5}$ log$_{3}$ 243

Solution,

We have, log$_{3}$ log$_{5}$ log$_{3}$ 243                    ---------------------------(1)

We know that, 243 = 3x3x3x3x3 = $3^{5}$     ---------------------------(2)

On putting (2) in (1), we get,

⇒ log$_{3}$ log$_{5}$ log$_{3}$ $3^{5}$

using the property of log, log$_{a}$$a^{m}$ = m

⇒ log$_{3}$ log$_{5}$ 5

using the property of log, log$_{a}$$a^{}$ = 1

⇒ log$_{3}$ 1

using the property of log, log$_{a}$ 1 = 0

⇒ 0.

Therefore, the value of log$_{3}$ log$_{5}$ log$_{3}$ 243 is 0.