Question

7^log^4^ 48/ 7 ^log^4 ^3

Answer 1

7^(log4(48)-log4(3))= 7^(log4(48/3))= 7^(log4(16))= 7²= 49

Answer 2

To simplify the expression 7^(log^4(48)/7)^(log^4(3)), we first need to evaluate the logarithms.

Step 1: Evaluate log^4(48) To find log^4(48), we need to determine what power we need to raise 4 to in order to get 48. 4^3 = 64 (4 * 4 * 4 = 64) 4^4 = 256 (4 * 4 * 4 * 4 = 256)

Since 48 is between 64 and 256, we can estimate that 48 is between 4^3 and 4^4.

Now, let's find the logarithm base 4 of 48: log^4(48) ≈ log(48)/log(4)

Using a calculator, log(48) ≈ 1.68 (rounded to two decimal places) and log(4) = 1.

log^4(48) ≈ 1.68/1 ≈ 1.68.

Step 2: Evaluate log^4(3) Similarly, we'll find log^4(3):

log^4(3) ≈ log(3)/log(4)

Using a calculator, log(3) ≈ 0.48 (rounded to two decimal places).

log^4(3) ≈ 0.48/1 ≈ 0.48.

Step 3: Substitute the values back into the original expression

7^(log^4(48)/7)^(log^4(3)) becomes 7^(1.68/7)^(0.48).

Step 4: Simplify further

7^(1.68/7) can be simplified as (7^1.68)^(1/7).

Now, we can use a calculator to evaluate 7^1.68 ≈ 12.12 (rounded to two decimal places).

(7^1.68)^(1/7) ≈ 12.12^(1/7) ≈ 1.80 (rounded to two decimal places).

Step 5: Final result

So, the final simplified expression is approximately 1.80.