Question

2. Solve for x. More than one answer may be correct. Select all correct choices.*

Answer 1

Answer:

None of these are correct

The value x = 35 is correct

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