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Logarithms — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSLogarithms3 Marks
Question
Prove that : If $a \log b + b \log a - 1 = 0,$ then $b^a.a^b= 10$
✓

Answer

Given that $\log b + b \log a - 1 = 0$
$\Rightarrow a \log b + b \log a = 1$
$\Rightarrow \log b^a + loga^b =1$
$\Rightarrow \log b^a + \log a^b = \log 10$
$\Rightarrow \log ( b^a . a^b ) = \log 10$
$\Rightarrow b^a . a^b = 10$

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