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apologiabiology
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:

Value of n is 9.70 (approx.)

Step-by-step explanation:

Given Expression: [tex]11^{n-8}-5=54[/tex]

We need to solve the given expression.

Consider,

[tex]11^{n-8}-5=54[/tex]

transpose 5 to RHS

[tex]11^{n-8}=54+5[/tex]

[tex]11^{n-8}=59[/tex]

take log on both sides.

[tex]log\,11^{n-8}=log\,59[/tex]

[tex](n-8)log\,11=1.77[/tex]

[tex](n-8)\times1.04=1.77[/tex]

[tex]n-8=\frac{1.77}{1.04}[/tex]

[tex]n=1.70+8[/tex]

[tex]n=9.70[/tex]

Therefore, Value of n is 9.70 (approx.)

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