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Solve the equation logₓ 10= 3/1
A) x=10
B) x=³√10
C) x=1/10
D) x=3​
.

User Erasmia
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8.3k points

1 Answer

3 votes

Final answer:

To solve logx 10 = 3, we recognize that log means the power to which we raise the base 'x' to get 10. Since the log is 3, x must be the cube root of 10. Therefore, option B) x = ³√10 is the correct answer.

Step-by-step explanation:

The student has asked to solve the equation logx 10 = 3. To solve this, we need to understand the definition of a logarithm. A logarithm is the exponent by which a base, in this case 'x', must be raised to yield a certain number, which is 10 here. So if logx 10 = 3, it means that x raised to the power of 3 equals 10 (x³ = 10).

To find the value of x, we essentially need to take the cube root of 10. This is because raising x to the third power gives us 10, so we must reverse this operation. Hence, x = ³√10, which can also be written as x = 101/3. When you use a calculator to find 10^(1/3), it confirms that x is indeed the cube root of 10.

Therefore, based on the given options, the correct answer is B) x = ³√10. To solve logx 10 = 3, we recognize that log means the power to which we raise the base 'x' to get 10. Since the log is 3, x must be the cube root of 10. Therefore, option B) x = ³√10 is the correct answer.

User Clint Miller
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8.2k points
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