Question

if log3=0.4771 then the number of digits in 3^20 is​

Answer 1

10 digits

y = 3²⁰

log y = log 3²⁰

log y = 20 log 3

log y = 20 × 0.4771

log y = 9.542

y = anti log ( 9.542 )

hence....

y contains ( 9 + 1 ) digits

therefore....

number of digits in 3²⁰ is 10

Answer 2

If log 3 = 0.4771 then the number of digits in 3²⁰ is 10

Given :

log 3 = 0.4771

To find :

The number of digits in 3²⁰

Solution :

Step 1 of 2 :

Write down the given expression

Let x = 3²⁰

Taking logarithm in both sides we get

$\displaystyle \sf{ log \: x = log \: {3}^{20} }$

$\displaystyle \sf{ \implies log \: x = 20 \: log \: 3 }$

Step 2 of 2 :

Find number of digits in 3²⁰

$\displaystyle \sf{ \implies log \: x = 20 \: \times 0.4771 }$

$\displaystyle \sf{ \implies log \: x = 9.542 }$

Taking anti logarithm in both sides we get

$\displaystyle \sf{ x = {10}^{9.542} }$

$\displaystyle \sf{ \implies x = {10}^{9} \times {10}^{0.542}}$

$\displaystyle \sf{ \implies x = m \times {10}^{9} \: \: (where \: m = {10}^{0.542} < 10)}$

Since the exponent of 10 is 9

Hence the number of digits in 3²⁰

= 9 + 1

= 10