Logarithms

Question

Log2^{3 +} log2 (x-10) =2

Answer 1

Assuming this should actually read:

 

Log₂3 + log₂ (x-10) =2

 

 

Utilize the addition theorem for logs in order to combine the two logs on the left side of the equation:

 

----> Log₂ [(3) * (x-10)] = 2

 

Use the definition of logs to remove the Log from the equation (Log_ab=c  means  a^c=b)

---->2² = (3)(x-10)

 

Solve using algebra

----> 2² = (3)(x-10)   (calculate the power)

----> 4 = 3(x-10)       (distribute the 3)

----> 4 = 3x-30          (combine like terms by adding 30 to both sides)

----> 34 = 3x            (isolate the variable by dividing both sides by 3)

----> 34/x = x  ***