## Trending News

Promoted

# Solve the Logarithms with a base of 10?

what steps do i take to solve this and then turn it into a base 10 log?

### 3 Answers

Relevance

- JimLv 72 years ago
2^(-3 x) = 11^(-x - 5)

Take reciprocals of both sides:

2^(3x) = 11^(x + 5)

Take the logarithm of both sides and use the identity log(a^b) = b log(a):

3 log(2) x = log(11) (x + 5)

Expand out terms of the right hand side:

3 log(2) x = log(11) x + 5 log(11)

Subtract x log(11) from both sides:

(3 log(2) - log(11)) x = 5 log(11)

Divide both sides by 3 log(2) - log(11):

x = (5 log(11))/(3 log(2) - log(11))

- az_lenderLv 72 years ago
2^(-3x) = 11^(-x-5) =>

2^(3x) = 11^(x+5) =>

(3x) * log(2) = (x+5) * log(11) =>

x * [3*log(2) - log(11)] = 5*log(11) =>

x * [log(8/11)] = 5*log(11) =>

x = 5*log(11)/log(8/11)

Still have questions? Get your answers by asking now.