# How do you evaluate #log_49 7#?

##### 4 Answers

#### Explanation:

Written in this form, the question being asked is.."How can I get 7 from 49?"

The answer is, by finding the square root. Another way of saying "square root" is the power of

In maths:

Therefore

We can also ask "Which power of 49 is equal to 7?:

#### Explanation:

then

Have a look at https://socratic.org/s/awwES2YN

#### Explanation:

Set

Write as

Take logs to base 10 of each side of Equation(1)

This is the same as:

#### Explanation:

Let:

#x=log_49 7#

By the definition of logarithms, this can be rewritten as:

#49^x=7#

Write

#(7^2)^x=7#

Simplify

#7^(2x)=7#

Recall that

#7^(2x)=7^1#

Since the powers are equal, we know their bases also must be equal:

#2x=1#

#x=1/2#