Question

How to solve 11^(n-8) - 5 =54

Answer 1

11ⁿ⁻⁸-5=54
add 5 both sides
11ⁿ⁻⁸=59
take log₁₁ bot sides
log₁₁11ⁿ⁻⁸=log₁₁59
n-8=log₁₁59
add 8 to both sides
n=(log₁₁59)+8

Answer 2

Value of n is 9.70 (approx.)

Explanation:

Given Expression:
`11^(n-8)-5=54`

We need to solve the given expression.

Consider,

`11^(n-8)-5=54`

transpose 5 to RHS

`11^(n-8)=54+5`

`11^(n-8)=59`

take log on both sides.

`log\,11^(n-8)=log\,59`

`(n-8)log\,11=1.77`

`(n-8)*1.04=1.77`

`n-8=(1.77)/(1.04)`

`n=1.70+8`

`n=9.70`

Therefore, Value of n is 9.70 (approx.)