Indices problem

[lingping7]

How many digits are there in the answer when 2¹²⁰ X 5¹²³when the answer is written without indices.
I have no clue how to do this problem.

Thanks in advance

 

[Deleted member 4993]

How many digits are there in the answer when 2¹²⁰ X 5¹²³when the answer is written without indices.
I have no clue how to do this problem.

Thanks in advance

ow many digits are there in:

2¹ * 5¹

2² * 5²

2³ * 5³

.
.
.
2¹²⁰ * 5¹²⁰

Now think some more.....

 

[lampat]

No. of Digit in \(\displaystyle 2^{120} = \lfloor 120 \times \log_{10}\left(2\right)\rfloor +1 = \)

Where \(\displaystyle \lfloor x \rfloor = \) floor function of \(\displaystyle x\)

 

[lingping7]

ow many digits are there in:

2¹ * 5¹

2² * 5²

2³ * 5³

.
.
.
2¹²⁰ * 5¹²⁰

Now think some more.....

So you mean to say I make 2¹²⁰ * 5^{123 =} 2¹²⁰ * 5¹²⁰ * 5³
Then 5³ * (2 * 5)¹²⁰
125 * 10¹²⁰
So answer is 125 followed by 120 0's
123 digits?

 

[Deleted member 4993]

So you mean to say I make 2¹²⁰ * 5^{123 =} 2¹²⁰ * 5¹²⁰ * 5³
Then 5³ * (2 * 5)¹²⁰
125 * 10¹²⁰
So answer is 125 followed by 120 0's
123 digits?

That's it..... just a little thinking .... that's all is needed!