Question

Solve for x in the equation below.

Round your answer to the nearest hundredth.
Do not round any intermediate computations.

Answer 1

x ≈ 0.07(NEAREST HUNDREDTH)

Explanation:

Given,

11^8x = 4

Solving for x:

Take logarithm of both sides,

• log(11^8x) = log(4)

Can be rewritten as,

• 8x * log(11) = log 4

Transposing log to the RHS,

• 8x = log(4)/log(11)
• 8x = 4/11
• 8x = 0.57813

Transposing 8 to RHS,

• x = 0.57813/8
• x = 0.0722266
• x ≈ 0.07 (Nearest hundredth)

Answer 2

Explanation:

11^(8x) = 4

we need a logarithm to solve for variables in an exponent.

in this case we start with the logarithm to the base of 11 :

8x = log11(4)

x = log11(4)/8

how can we get log11 ?

remember,

loga(b) = logc(b)/logc(a)

and so,

x = (log10(4)/log10(11)) / 8 = 0.072266207... ≈ 0.07