# log x^2 - log 10 - 3 = 0

hala718 | Certified Educator

log x^2 - log 10 -3 =0

We know that:

log 10 =1

log x^2 = 2 logx

==> 2log x -1 -3 =0

==> 2log x -4 =0

Move 4 to the right side:

==> 2log x = 4

Divide by 2

==> log x = 4/2 =2

==> x = 10^2 = 100

The answer is x = 100

kjcdb8er | Certified Educator

Here, we assume that log means log base 10. This means that log 10 = 1

log x^2 - log 10 - 3 = 0

2 log x - 1 - 3 = 0

2 log x = 4

log x = 2

This means that 10^2 = x, by the definition of the logarithm

tonys538 | Student

The equation log x^2 - log 10 - 3 = 0 has to be solved.

As log refers to logarithm to the base 10, write all the terms as logarithm.

3 = log_10 1000

This gives an equation

log x^2 - log 10 - log 1000 = 0

Now use the property of logarithm log a - log b = log(a/b)

log(x^2/(10*1000)) = 0

If log_b x = y, x = b^y

Here, we get

x^2/10000 = 10^0

x^2 = 10000

x = 100

The solution of the equation is x = 100

jucinho | Student

log10=1

logx^2-1-3=0

logx^2=4

x^2=10^4=10000

x=100; x=-100

giorgiana1976 | Student

First, we'll add log 10 + 3, both sides of the equation:

log x^2 = log 10 + 3

We could write 3 = 3*1 = 3*log 10

log x^2 = log 10 + 3*log 10

We'll factorize:

log x^2 = log 10*(1+3)

log x^2 = 4*log 10

We'll use the power property of logarithms:

log x^2 = log 10^4

We'll use the one to one property and we'll get:

x^2 = 10^4

x1 = +sqrt 10^4

x1 = +100

x2 = -100

For log x^2 to exist, x>0, so the equation will have only one solution, namely x = +100.

neela | Student

To solve logx^2-log10-3 =0

Solution:

logx^2-log10-3 = 0

logx^2 = log10 +3 = log1 +log10^3  =log10*10^3, as loga+logb = log(ab).

logx^2 = log10^4. Take the antilogarithm.

x^2 =10^4

x= 10^2 = 100