What is the definition of a logarithm?

\( k+9, k-6 \) र 4 एउटा गुणोत्तर अनुक्रमका \( k+9, k-6 \) and 4 are the three terms of a geometric progression (i) \( k \) को मान पत्ता लगाउनुहोस् । (Find the value of \( k \).) (ii) समान अनुपात पत्ता लगाउनुहोस् । (Find the common ratio.) (iii) चौथो पद पत्ता लगाउनुहोस् । (Find the value of fourth term.) odel 3 Problems based on finding the position of a given term i)

What does the exponent in an expression indicate?

Three quantities \( t, x \) and \( y \) are such that \( t \) varies directly as \( x \) and invisely as the square root of \( y \). Find the percentage decrease in \( t \) if \( x \) decreases by \( 44 \% \).

212 / बीजगणित (Algebra) 24. यदि \( 4,2 x-4, \ldots \ldots, 64,21 x+2 \) एउटा गुणोत्तर अनुक्रमको पदहरू भए, If \( 4,2 x-4, \ldots \ldots, 64,21 x+2 \) are the terms of geometric sequence (i) \( x \) को मान पत्ता लगाउनुहोस् । (Find the value of \( x \).) (ii) समान अनुपात पत्ता लगाउनुहोस् । (Find the common ratio.) (iii) चौथो पद पत्ता लगाउनुहोस् । (Find the value of fourth term.)

\( \left. \begin{array} { l } { ( x + y ) ^ { 3 } = z } \\ { ( y + z ) ^ { 3 } = x } \\ { ( z + x ) ^ { 3 } = y } \end{array} \right. \)