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Sagot :
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]
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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