7 ^ - (log_7(8) × log_8(7) * 7 log_7(2)

Answer 1

To solve this expression, we need to simplify each term individually and then perform the operations.

Let's simplify each term step by step:

1) log_7(8) can be written as log(8) / log(7) using the change of base formula. We can use a calculator to calculate the value of log(8) and log(7) separately.

log(8) ≈ 0.9031
log(7) ≈ 0.8451

So, log_7(8) ≈ 0.9031 / 0.8451 ≈ 1.0687

2) log_8(7) can be written as log(7) / log(8).

log(7) ≈ 0.8451
log(8) ≈ 0.9031

So, log_8(7) ≈ 0.8451 / 0.9031 ≈ 0.9360

3) 7 log_7(2) can be simplified using the property: a log_a(p) = p.

So, 7 log_7(2) = 7*(2) = 14.

Now, let's substitute these simplified values back into the original expression:

7^(- (log_7(8) × log_8(7) * 7 log_7(2))

= 7^(- (1.0687 × 0.9360 * 14))

= 7^(- (14.0166))

≈ 0.000000004404

Therefore, 7^(- (log_7(8) × log_8(7) * 7 log_7(2)) ≈ 0.000000004404.