# What is solution of the equation : log(4x+16) - log100 = log16 - 2*log2

Tushar Chandra | Certified Educator

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The equation to be solved is: log(4x+16) - log100 = log16 - 2log2

Use the relations: log a - log b = log(a/b), log + log b = log a*b  and n*log a = log a^n

log(4x+16) - log100 = log16 - 2log2

=> log(4x+16) = log100 + log16 - log 2^2

=> log(4x+16) = log 100 + log 16 - log 4

=> log(4x+16) = log 100*16/4

=> log(4x+16) = log 400

We can equate 4x + 16 = 400

=> x + 4 = 100

=> x = 96

The required value is x = 96

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giorgiana1976 | Student

We'll apply quotient rule, both sides of the equation:

log [(4x+16)/100] = log(16/4)

Since the bases are matching, we'll apply one to one property:

[(4x+16)/100] = 16/4

[(4x+16)/100] = 4

We'll multiply by 100 both sides:

4x + 16 = 4*100

We'll divide by 4:

x + 4 = 100

We'll subtract 4:

x = 100 - 4

x = 96

The constraint of existence of logarithm is 4x+16>0

4x>-16

x>-4

The interval of admissible values for x is (-4 ; +infinite).

Since the value of x is in the rangle of admissible values, we'll accept as solution of the equation x = 96.