Question

Log_{7} 49^{4}вычислить

Answer 1

$\log_{7} 49^{4}=\log_7(7^{2})^4=\log_7 7^8=8\log_77=8\cdot1=8$

Answer 2

$log_{7}{49^4}=log_{7}{(7^2)^4}=log_{7}{7^8}=8$

Answer 3

To calculate the expression log base 7 of 49 raised to the power of 4, we can use the logarithmic property that states log base a of b raised to the power of c is equal to c times log base a of b.

Therefore, we have:

log_{7} 49^{4} = 4 * log_{7} 49

Since 49 is equal to 7 raised to the power of 2 (49 = 7^2), we can simplify further:

4 * log_{7} 49 = 4 * log_{7} (7^2)

Using another logarithmic property, log base a of a^c is equal to c, we can simplify the expression:

4 * log_{7} (7^2) = 4 * 2

Finally, we get:

log_{7} 49^{4} = 8