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.
B i
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Font Family
- AAT A
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Answers
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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