How do you evaluate log_49 7?

4 Answers
EZ as pi
Jul 27, 2016

log_49 7 = 1/2

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 1/2.

In maths: log_49 = x " "rArr 49^x = 7

49^(1/2) = 7

Therefore log_49 7 = 1/2

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

Cesareo R.
Jul 27, 2016

1/2

Explanation:

log_a b = (log_e b)/log_e a

then

log_{49}7 = (log_e 7)/(log_e 7^2)=(log_e7)/(2log_e 7)=1/2

Tony B
Jul 27, 2016

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

x=0.5

Explanation:

color(blue)("Derived by calculation")

Set log_49(7)=x

Write as 49^x=7.........................Equation(1)

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

log_10(49^x)=log_10(7)

This is the same as:

xlog_10(49)=log_10(7)

x=log_10(7)/log_10(49)

x=0.5

mason m
Jul 27, 2016

1/2

Explanation:

Let:

x=log_49 7

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

49^x=7

Write 49 as 7^2:

(7^2)^x=7

Simplify (7^2)^x using the rule (a^b)^b=a^(bc):

7^(2x)=7

Recall that 7=7^1:

7^(2x)=7^1

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

2x=1

x=1/2

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