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Solve the following equation for x:
log10 x - log10 √x = = 2 logx 10
log10 x - log10 √x = = 2 logx 10
- a)185
- b)200
- c)190
- d)100
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Solve the following equation for x:log10 x - log10 √x = = 2 logx...
Understanding the Equation
To solve the equation:
log10 x - log10 √x = 2 logx 10
We can simplify this step by step.
Step 1: Simplifying the Left Side
Using the properties of logarithms:
- log10 √x = log10 (x^(1/2)) = (1/2) log10 x
So, the left side becomes:
log10 x - (1/2) log10 x = (1/2) log10 x
Step 2: Simplifying the Right Side
The right side can be rewritten using the change of base formula:
logx 10 = 1 / log10 x
Thus,
2 logx 10 = 2 / log10 x
Step 3: Setting the Equation
Now, we can set the simplified left side equal to the simplified right side:
(1/2) log10 x = 2 / log10 x
Step 4: Cross Multiplying
Multiplying both sides by log10 x yields:
(log10 x)^2 = 4
Taking the square root gives us:
log10 x = ±2
Step 5: Finding x
Considering the positive root (logarithm is positive for positive x):
log10 x = 2 implies that:
x = 10^2 = 100
Final Answer
The correct answer is option 'D': 100. This value satisfies the original equation and follows the logarithmic properties accurately.
To solve the equation:
log10 x - log10 √x = 2 logx 10
We can simplify this step by step.
Step 1: Simplifying the Left Side
Using the properties of logarithms:
- log10 √x = log10 (x^(1/2)) = (1/2) log10 x
So, the left side becomes:
log10 x - (1/2) log10 x = (1/2) log10 x
Step 2: Simplifying the Right Side
The right side can be rewritten using the change of base formula:
logx 10 = 1 / log10 x
Thus,
2 logx 10 = 2 / log10 x
Step 3: Setting the Equation
Now, we can set the simplified left side equal to the simplified right side:
(1/2) log10 x = 2 / log10 x
Step 4: Cross Multiplying
Multiplying both sides by log10 x yields:
(log10 x)^2 = 4
Taking the square root gives us:
log10 x = ±2
Step 5: Finding x
Considering the positive root (logarithm is positive for positive x):
log10 x = 2 implies that:
x = 10^2 = 100
Final Answer
The correct answer is option 'D': 100. This value satisfies the original equation and follows the logarithmic properties accurately.
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Solve the following equation for x:log10 x - log10 √x = = 2 logx 10a)185b)200c)190d)100Correct answer is option 'D'. Can you explain this answer?
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