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A student showed the steps below while solving the equation 14 = log Subscript 5 Baseline (2 x minus 3) by graphing.

Step 1:
Write a system of equations: y 1 = 14; y 2 = log Subscript 5 Baseline (2 x minus 3)
Step 2: Use the change of base formula to rewrite the equations:
y 1 = log 14; y 2 = StartFraction log (2 x minus 3) Over log 5 EndFraction
Step 3: Graph the two equations:
On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (2, 0). A horizontal straight line is at y = 1.
Step 4: Identify the x-value at the point of intersection:
x almost-equals 4.5

In which step did the student make the first error?

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Answer

Step 4

Explanation:

The equation the student solved is

[tex] \frac{1}{4} =\log_{5}(2x - 5) [/tex]

His first step is to write the system :

[tex]y_1 = \frac{1}{4} \\ y_2 = \log_{2}(2x - 3) [/tex]

This is correct

Step 2:

He used change of base formula to obtain:

[tex]y_1 = \frac{1}{4} \\ y_2 = \frac{ \log(2x - 3) }{ \log(5) } [/tex]

This is also correct

Step 3:

He mistakenly graphed

[tex]y_1=1[/tex]

instead of

[tex]y_1= \frac{1}{4} [/tex]

The mistake occurred in step 3.

Answer:

step 2

Step-by-step explanation:

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