Question

x
purt
harte a borbvsdghhxdhj​

Answer 1

Solution

$5^{2 + log_510 }$

$= 5^{2} \times 5^{ log_510}$

$\tt [ \because a^{m + n}= a^m \times a^n ]$

$= 25 \times 10$

$\tt [ \because a^{ log_an } = n ]$

$= 25 \times 10$

$= 250$

Hence the answer is 250.

Answer 2

Question :-

${ \star \: } \large{\sf{x = { \red{5 }\: }^{2 + \orange{log \: _{5}(10)} } } \: \green{find }\: x} \: \:$

Answer :-

$\green{\implies \:} \red{ \boxed{ \green{ \boxed{ \orange{\boxed{ \sf{ \red{x} \: = \green{250}}}}}}}} \:$

Solution :-

We have ,

$\rightarrow \large{ \sf{x = { \red{5 }\: }^{2 + \orange{log \: _{5}(10)} } }} \: \: \: \\ \\ \: \because \large{ \boxed{\sf{ \red{ {a}^{m + n}} = \orange{ {a}^{m} \times {a}^{n} }}}}\\ \\ \pink{\therefore} \\ \rightarrow \large{ \sf{ \pink{x }= \green{ {5}^{2}} \times { \blue{5 \: }}^{ \red{log \: _{5}(10)} } } }\\ \\ \blue{ \because }\large{ \boxed{\sf{ {b \: }^{ log_{b}(a) } } = a} }\\ \\ \red{ \therefore }\\ \rightarrow \large{\sf{x = \red{ 25 \times } \green{10}}} \\ \\ \rightarrow \large{ \red{ \boxed{ \blue{\boxed{ \orange{\boxed{ \sf{ \red{x} \: = \green{250}}}}}}}}}$

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