Question
Real Tutor Solution
Tutor-Verified Answer
Answer
Tenglamaning yechimi: \( x = 0 \)
Solution
Berilgan tenglama:
\[ 7^{x} \cdot 8^{x} = 1 \]
Avvalo, eksponentlarni birlashtiramiz:
\[ (7 \cdot 8)^{x} = 56^{x} = 1 \]
Har qanday $a \neq 0$ son uchun $a^{0} = 1$ bo'lishi sababli, tenglama quyidagi shartni beradi:
\[ x = 0 \]
Shunday qilib, tenglamaning yechimi:
\[ x = 0 \]
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Simplify this solution Beyond the Answer
To solve the equation \( 7^{x} \cdot 8^{x}=1 \), we can rewrite it as \( (7 \cdot 8)^{x} = 1 \). Since \( 7 \cdot 8 = 56 \), we have \( 56^{x} = 1 \). Recall that for any non-zero base \( a \), \( a^{0} = 1 \). Therefore, \( x \) must be \( 0 \) because \( 56^{0} = 1 \). Thus, the solution is \( x = 0 \).
