How to solve these exponential and logarithmic equations?

Question

So I need to know the steps to take and the work to do to get to these answers. Thanks :)
1. 2^x = 14 Ans = 3.807
2. 3^(x+2) = 81 Ans. = 2
3. log(x+8) = 1 + log(x-10)

Answer 1

1). 2^x = 14

Apply log each side.

log 2^x = log 14

Algebraic logarithm identities or laws: logAⁿ = n logA

logarithm table in log14=1.1461 and log2 = 0.3010.

x log2 = log14

x(0.3010) = 1.1461

Divide each side by 0.3010.

x = (1.1461)/(0.3010) = 3.8076

Therefore x = 3.8076

Answer 2

2). 3^x+2 = 81

Mathematics formula: A^m+n = A^mAⁿ

So, (3^x)( 3²) = 81

(3^x)( 9) = 81

Divide each side by 9.

3^x = 9

3^x = 3²

Apply log each side.

log 3^x = log 3²

Algebraic logarithm identities or laws: logAⁿ = n

x log3 = 2log3

Cacel common terms.

x = 2

Therefore x = 2.

Answer 3

3).  log(x+8) = 1 + log(x-10)

Logarithm table in log10 = 1.

log(x+8) = log10 + log(x-10)

Using simpler operation: logA+logB = log(AB)

log(x+8) = log10(x-10)

Cancel common term 'log'

x+8 = 10(x-10)

Distribute terms using distributive property:  a( b + c) = ab + ac

x-8 = 10x - 100

Subtract x from each side.

-8 = 9x - 100

Add 100 to each side.

92 = 9x

Divide each side by 9.

x = 10.22