i assume this is log to the base 10

log4 + 2log5

= log4 + log(5^2) ............................since n*log(x) = log(x^n)

= log4 + log25

= log(4*25) ....................................since log(x) + log(y) = log(xy)

= log100

= 2

are these logs to the base 5?

"Solve the equation: log5x-3log52=log53"

if so,

log[5]x-3log[5]2=log[5]3

= log[5]x - log[5]2^3 = log[5]3 ...................since n*log(x) = log(x^n), i changed 3log[5]2 to log[5]2^3

= log[5]x - log[5]8 = log[5]3

= log[5]8x = log[5]3

now we can equate what's being logged.............since if logA = logB, then A = B, pretty intuitive i think

=> 8x = 3

=> x = 3/8

i suppose this is log to the base x, you need to type these questions clearer, include the base in [] and let us know that's what it means

Also, "Solve the equation: logx32= 5"

But as for this one, I tried and got as far as this:

x^5 = 32

log[x]32 = 5

=> x^5 = 32 ...................................since if log[a]b = c, then a^c = b ...this is a fundamental law of logarithms, in fact, its the definition of a log

=> x = 32^(1/5)

=> x = 2

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if you have any questions, or if i misinterpreted any of the problems (since you did not identify the bases properly), don't hesitate to say so