when to know whether to sub a letter to something?
like subbing u into 3^x

is that change of base at the log part? im quite confused with change of base especially in this question as i was stucked there
can you explain to me change of base fornula? will really appreciate it :)

The substitution helps us to look at the equation more easily, because the structure of the equation to be solved appears to be quadratic with a squared term existing. Using the substitution will allow the equation to be really quadratic.

The solving of the exponential part can be solved by taking logs on both sides. It’s not really a change of base as the equation to solve, 3^x = 5, is not in logarithmic form. I took log to base 10 on both sides of the equation in this case.

You can also do a change of base, however, by noting that writing 3^x = 5 in the equivalent logarithmic form gets us x = log3 5, which we can then use change of base to base 10 to get lg 5 / lg 3 which you will then put in the calculator.

for change of base formula do we just sub in any numbers as the base or theres a standard procedure to determine what number to use as the base

Depending on the question, some bases are more effective than others. Base 10 and e are for calculator use. Base 2, 3 etc are for “non calculator” working purposes.

bases 2,3,5 etc are usually used when the question ask : when log2 7 = 5, solve......?

“Solve” are mainly bases 10 and e.

If the question says
“given that log2 x = k, express log4 x in terms of k”

Then base 2 is more appropriate.