Question

plezz solve it
surds and indices​

Answer 1

Answer:

10n-m-1

Step-by-step explanation:

We have been given that 2=10

m

and 3=10

n

We know,

2×10

3

=0.15

⇒

10

m

×10

1

10

n

=0.15

⇒

10

m+1

10

n

=0.15 [x

m

×x

n

=x

m+n

]

⇒ 10

n−(m+1)

=0.15 [

x

n

x

m

=x

m−n

]

∴ 0.15=10

n−m−1

Answer 2

$\large 12 = n$

Step-by-step explanation:

Given -

• $\large {3}^{10} \times {27}^{2} = {9}^{2} \times {3}^{n}$

To find -

• The value of 'n'.

Solution -

$\large {3}^{10} \times {27}^{2} = {9}^{2} \times {3}^{n}$

$⟹ \large {3}^{10} \times ({3}^{3} )^{2} = ({3}^{2} )^{2} \times {3}^{n}$

$⟹ \large {3}^{10} \times {3}^{3 × 2} = {3}^{2 × 2} \times {3}^{n}$

$⟹ \large {3}^{10} \times {3}^{6} = {3}^{4} \times {3}^{n}$

$⟹ \large {3}^{10 + 6} = {3}^{4 + n}$

$⟹ \large {3}^{16} = {3}^{4 + n}$

$\large On \: \: equating \: ,$

$⟹\large 16 = 4 + n$

$⟹ \large 16 - 4 = n$

$⟹ \large\bf \green{ \boxed{12 = n}}$