Question

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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= = =

Answer 1

None of these are correct

The value x = 35 is correct

Step-by-step explanation:

Step(i):-

Given

`log^(2) _(10) + log^((x+5)) _(10) = 2`

We will apply logarithmic formula

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

logₓ a = b

⇒ a = xᵇ

Step(ii):-

`log^(2) _(10) + log^((x+5)) _(10) = 2`

`log^(2(x+15)) _(10) = 2`

⇒ 2 ( x + 15 ) = 10²

⇒ 2 x + 30 = 100

⇒ 2 x = 70

⇒ x = 35

Final answer:-

x = 35

Verification:-

`log^(2) _(10) + log^((x+5)) _(10) = 2`

`log^(2(35+15)) _(10) = 2`

`log^((100)) _(10) = 2`

`log^{(10)^(2) } _(10) = 2`

log x ⁿ = n log x

2 log¹⁰ ₁₀ = 2

2 = 2 ( log¹⁰ ₁₀ = 1