18^10=4^5*3^x Algebra 2 help

Question

Must be solved without using a calculator.

Answer 1

18¹⁰ can be written as (2 • 3 • 3)¹⁰ which equals 2¹⁰ • 3¹⁰ • 3¹⁰

When like bases are being multiplied, keep the base the same and add the exponents. So:

3¹⁰ • 3¹⁰ = 3^{10 + 10} = 3²⁰

So now 18¹⁰ = 2¹⁰ • 3²⁰

4⁵ • 3^x =

2⁵ • 2⁵ • 3^x =

2¹⁰ • 3^x

18¹⁰ = 4⁵ • 3^x

2¹⁰ • 3²⁰ = 2¹⁰ • 3^x

So x = 20

Answer 2

18¹⁰ = 4⁵·3^x

(2·3²)¹⁰ = (2²)⁵·3^x

2¹⁰·3²⁰ = 2¹⁰·3^x

(2¹⁰·3²⁰)/2¹⁰ = 3^x

3²⁰ = 3^x

Since the bases are the same (3), the exponents must be the same:

20 = x