Question

if log10 3 = 0.477 then find the no. of digits in 3^40​

Answer 1

Answer:from the equation log₁₀3 =0.477

i.e 3=10^0.477

3=2.999999

so that 2.999^40=

10637694969200170000

No of digit is 20

Step-by-step explanation:

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \red{ \mid}}}}}}}}$

$\underline{ \bold{ \: \: GIVEN \: : }} \to \: \: \: \: \: \: \: \bold{ log_{10}3 =0 .477} \\ \\ \\ \underline{ \bold{ \: \: TO\: \: FIND\: \: }} \to \: \: \bold{No. \: \: of \: \: digit \: \: in \: \: 3 {}^{40} =? }$

$\bold{Let,} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 3 {}^{40} } \\ \\ \underline{\bold { \: \: Taking \: \: logarithm \: \: in \: \: both \: \: sides \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \bold{ log_{10}x = log_{10}(3 {}^{40} ) } \\ \\ \bold{ \Longrightarrow \: \: log_{10}x = 40 \: \: log_{10}3 } \\ \\ \bold{ \Longrightarrow \: \: log_{10}x = 40 \times 0.477} \\ \\ \bold{ \Longrightarrow \: \: log_{10}x = 19.08}$

$\bold{ \: \: Since ,\: \: the \: \: characteristic \: \: of \: \: } \\ \\ \: \: \: \: \: \: \bold{ log_{10}x = log_{10}3 {}^{40} = 19} \\ \\ \bold{So, \: \: the \: \: number \: \: of \: \: digit \: \: in} \\ \\ \bold{x = 3 {}^{40} = 19 + 1 = \boxed{ \bold{ \: \: 20 \: \: }}}$

$\bold{Hence,} \\ \\ \bold{If \: \: log_{10}3 = 0.477 \: \: , \: then \: \: the \: \: no. \: \: of \: \: } \\ \bold{digit \: \: in \: \: 3 {}^{40} = \underline{ \red{ \: \: 20 \: \: }}}$