Question

Which expressions are equivalent to the one below?check all that apply.

log5 125+log5 125

A.log5 15625
B.log5(5^6)
C.6
D.log 15625

Answer 1

A, B, and C

Explanation:

The expression
`log_(x)a=b` means "x to the power b equal a"

The expression
`log_5125+log_5125` means "5 raised to what power is 125" + "5 raised to what power is 125".

we know 5 to the power 3 is 125, so the expression is 3 + 3 = 6

A.

`log_(5)15,625` means 15 to "what power" gives us 15,625?

we know that 5 to the power 6 is 15625, so the expression
`log_(5)15,625` is equal to 6.

B.

The expression
`log_(5)(5^6)` means 5 raised to what power is "5 raised to 5"? Simple, the answer is 6

C.

this is 6 (given)

D.

Whenever we don't have a base for the log, it is taken as "base 10". So the expression Log 15625 means "10 raised to what power is 15,625"? It is approximately 4.19

Thus we can see that Option A, B, & C all are equal to the expression given (6).

Answer 2

The answers for the question shown above are the option A, the option B and the option C, which are:
A.log5(15625)
B.log5(5^6)
C.6
The explanation is shown below:
By applying the logarithms properties, you have:
A. log5(125)+log5(125)=log5(125)(125)=log5(15625)
B. log5(125)+log5(125)=log5(15625)=log5(5^6)
C. og5(125)+log5(125)=log5(15625)=log5(5^6)=6log5(5)=6