119k views
5 votes
Solve the equation: 7^n=343

2 Answers

3 votes

Answer:

n=3

Explanation:

7

n

=343

Use the rules of exponents and logarithms to solve the equation.

7

n

=343

Take the logarithm of both sides of the equation.

log(7

n

)=log(343)

The logarithm of a number raised to a power is the power times the logarithm of the number.

nlog(7)=log(343)

Divide both sides by log(7).

n=

log(7)

log(343)

By the change-of-base formula

log(b)

log(a)

=log

b

(a).

n=log

7

(343)

User ThatMatthew
by
7.8k points
5 votes

Answer is

7^n = 7^3

N=3

User Porjaz
by
8.9k points

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