Question

2log5 x+log5 100−2=0

Answer 1

2log5 (x) + log5 (100) - 2 = 0
log5 (x^2) + log5 (100) = 2
log5 (x^2*100) = 2
x^2*100 = 25
x^2 = 0,25
x = ±0,5
ОДЗ х>0, поэтому х = 0,5

Answer 2

2 log(5)x+log(5)100-2=0 ;x>0
2log(5)x+2 log(5)10-2=0

log(5)х+log(5)10-1=0
log(5)x+log(5)2+log(5)5-1=0
log(5)x+log(5)2=0
log(5)x=-log(5)2
ĺog(5)x=log(5)2^(-1)
x=1/2

Answer 3

To solve the logarithmic equation 2log5(x) + log5(100) - 2 = 0, we'll use some logarithmic properties to simplify it first and then solve for the variable x.

Step 1: Use logarithmic properties We know that log(a) + log(b) = log(a * b) and log(a) - log(b) = log(a / b). Using these properties, we can rewrite the equation as follows:

2log5(x) + log5(100) - 2 = 0

Rewrite log5(100) as log5(10^2) since 100 is equal to 10^2:

2log5(x) + log5(10^2) - 2 = 0

Now use the property: log(a^b) = b * log(a):

2log5(x) + 2log5(10) - 2 = 0

Step 2: Evaluate log5(10) We know that log5(10) is the exponent to which we raise 5 to get 10:

5^(log5(10)) = 10

Since 5^1 = 5, it means that log5(10) = 1.

Step 3: Substitute log5(10) back into the equation Now, we can replace log5(10) with 1 in the equation:

2log5(x) + 2(1) - 2 = 0

Simplify:

2log5(x) + 2 - 2 = 0

2log5(x) = 0

Step 4: Isolate the logarithm term Now, we want to isolate log5(x) on one side of the equation. To do this, we'll divide both sides by 2:

log5(x) = 0 / 2

log5(x) = 0

Step 5: Remove the logarithm and solve for x To remove the logarithm, we rewrite the equation in exponential form:

5^(log5(x)) = 5^0

Since any non-zero number raised to the power of 0 is 1, we get:

x = 1

So the solution to the equation is x = 1.