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2. Solve for x. More than one answer may be correct. Select all correct choices.*
log10 2 + log10 (x + 15) = 2
*This question is worth four points. In order to receive full credit, you must show your work or
justify your answer.
2= = -23
2 = -3
x = 5
= 3
x= -13
=
= -20
None of these are correct.
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2 Solve for x More than one answer may be correct Select all correct choices log10 2 log10 x 15 2 This question is worth four points In order to receive full cr class=

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Answer:

None of these are correct

The value x = 35 is correct

Explanation:

Step(i):-

Given

         [tex]log^{2} _{10} + log^{(x+5)} _{10} = 2[/tex]

We will apply logarithmic formula

log(a) + log (b) = log a b

  logₓ a = b

⇒   a = xᵇ

Step(ii):-

       [tex]log^{2} _{10} + log^{(x+5)} _{10} = 2[/tex]

    [tex]log^{2(x+15)} _{10} = 2[/tex]

⇒  2 ( x + 15 ) = 10²

⇒ 2 x + 30 = 100

⇒  2 x = 70

⇒  x = 35

Final answer:-

x = 35

Verification:-

 [tex]log^{2} _{10} + log^{(x+5)} _{10} = 2[/tex]

    [tex]log^{2(35+15)} _{10} = 2[/tex]

   [tex]log^{(100)} _{10} = 2[/tex]

  [tex]log^{(10)^{2} } _{10} = 2[/tex]

log x ⁿ = n log x

2 log¹⁰ ₁₀     = 2

2 =  2       (  log¹⁰ ₁₀ = 1

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