Math  /  Algebra

QuestionLab Homework Question 1, 4.4.C2
Fill in the blank so that the resulting statement is true. If 54x1=5115^{4 x-1}=5^{11}, then _=11\_=11
If 54x1=5115^{4 x-1}=5^{11}, then =11\square=11

Studdy Solution

STEP 1

1. The bases on both sides of the equation are the same (i.e., both are 55), which allows us to equate the exponents directly.
2. We need to solve for xx in the exponent equation 4x1=114x - 1 = 11.

STEP 2

1. Equate the exponents of both sides of the equation.
2. Solve the resulting linear equation for xx.

STEP 3

Given the equation 54x1=5115^{4x-1} = 5^{11}, we can equate the exponents because the bases are the same:
4x1=11 4x - 1 = 11

STEP 4

Solve the equation 4x1=114x - 1 = 11 for xx. Start by isolating the term with xx:
4x1+1=11+1 4x - 1 + 1 = 11 + 1 4x=12 4x = 12

STEP 5

Divide both sides of the equation by 44 to solve for xx:
x=124 x = \frac{12}{4} x=3 x = 3
The value of xx that satisfies the equation is 33.
Therefore, if 54x1=5115^{4x-1} = 5^{11}, then x=3x = 3.

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