Question

Which expression are equivalent to the one below? Check all that apply. Log5 5+log5 125

Answer 1

Answer:

B. 4

C. Log₅ 625

Step-by-step explanation:

When given the sum of two logarithms to the same base, let us say

LogₐB +LogₐC, Then, the sum is equivalent to Logₐ(B×C)

=Logₐ BC

The sum given in the question is Log₅5 + Log₅125

This is equivalent to Log₅(5×125)=Log₅625

Log₅625=4 (Since 625=5⁴, the log of 625 to base 5 is 4)

Answer 2

Answer:

4 and $log_5(625)$

Step-by-step explanation:

$log_5(5) + log_5(125)$

125 can be written as 5 times 5 times 5 is 5^3

$log_5(5) + log_5(125)$

$log_5(5) + log_5(5^3)$

Use log property and move the exponent before log

$log_5(5) + 3log_5(5)$

Both terms have log 5. so they are like terms

$log_5(5) + 3log_5(5)$

$4log_5(5)$ = 4

Also we can move 4 to the exponent

$alog(x)= log(x^a)$

$4log_5(5)$

$log_5(5)^4$

$log_5(625)$