Answered

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What is the solution of [tex]\log _x 729=3[/tex]?

A. 6
B. 9
C. 18
D. 81

Sagot :

GinnyAnswer
To solve the equation [tex]\(\log _x 729 = 3\)[/tex], we need to understand and manipulate logarithms. Here's a step-by-step solution:

1. Start with the given equation:
[tex]\[ \log_x 729 = 3 \][/tex]

2. Recall that [tex]\(\log_x 729 = 3\)[/tex] means that [tex]\(x\)[/tex] raised to the power of 3 equals 729. In exponential form, this is:
[tex]\[ x^3 = 729 \][/tex]

3. To solve for [tex]\(x\)[/tex], we need to find the cube root of 729:
[tex]\[ x = \sqrt[3]{729} \][/tex]

4. The cube root of 729 is 9 because:
[tex]\[ 9^3 = 9 \times 9 \times 9 = 729 \][/tex]

Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[ \boxed{9} \][/tex]
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