How to solve these log expressions?

i)

2log(x) = log(25) + 2

Converting everything into logs, we notice 2 = log100:
2log(x) = log(25) + log(100)

Using power law of logarithms, we notice 2log(x) = log(x^2):
log(x^2) = log(25) + log(100)

Using sum rule for logarithms, we notice log(25) + log(100) = log(25*100):
log(x^2) = log(2500)

Removing all logarithms (by raising everything to the power of 10):
x^2 = 2500
x = +/- 50

But since 2log(-50) doesn't exist, then x = +50


ii) log7 (7 is in small letters) 12 = x

Using the change of base rule for logarithms:
x = log(12)/log(7)

I hope this was helpful.

i)
2log(x) = log(25) + 2
2log(x) - log(25) = 2
2log(x) - log(5^2) = 2
2log(x) - 2log(5) = 2
2log(x/5) = 2
log(x/5) = 1
x/5 = 10^1
x/5 = 10
x = 50

ii)
log_7(12) = x
x = log_7(12)
x = log(12)/log(7) (= 1.2769894...)

Part ( i )
2 log x = log (25) + 2
log x ² - log 25 = 2
log ( x ² / 25 ) = 2
x ² / 25 = 100
x ² = 2500
x = 50

Part (ii)
log 12 = x ---------(log to base 7)
7^x = 12
x log 7 = log 12
x = log 12 / log 7
x = log 12
x = 1.277