SOLUTION: Solve log8(log5x) = 0. equation orientation: https://gyazo.com/06ba69cdf495e403774365fceb612d8e

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Question 1205555: Solve log8(log5x) = 0.
equation orientation: https://gyazo.com/06ba69cdf495e403774365fceb612d8e
Found 4 solutions by MathLover1, Theo, MathTherapy, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

......change to base








Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
your equation is log8(log5(x)) = 0

by log rules, this is true if and only if 8^0 = log5(x)

since 8^0 = 1, then you get log5(x) = 1

this is true if and only if 5^1 = x

this makes x = 5

you get log8(log5(5)) = 0

by log base conversion rules, log5(5) = log(5)/log(5) = 1

this gets you log8(1) = 0

by log base conversion rules, this gets you log(1)/log(8) = 0

since log(1) = 0, this becomes 0/log(8) = 0, confirming the original equation is correct.

your solution is that x = 5.

the general log base conversion rule is loga(x) = logb(x)/logb(a)

it is most often use to convert from any log base to the base 10 or to the base e.

in your calsulator, log to the base 10 is the log function and log to the base e is the ln function.

two simple examples will show you how this work.

2^3 = 32 if and only if log2(32) = 5.

that is a basic log rule which you need to know, if you didn't already.

how to confirm this is true.

you want to find log2(32) to see that it is equal to 5.

in your calculator, you would convert from base 2 to either base 10 or base e.

converting to base 10, you get log2(32) = log(32)/log(2) = 5

converting to base e (the ln function), you get log2(32) = ln(32)/ln(2) = 5.

it works like a charm.

here is a reference on log rules.

https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/














Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Solve log8(log5x) = 0.
equation orientation: https://gyazo.com/06ba69cdf495e403774365fceb612d8e

log8[log5(x)] = 0
      log5(x) = 80 ----- Converting to EXPONENTIAL form
      log5(x) = 1
            x = 51 ----- Converting to EXPONENTIAL form

Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!




The format of the given equation is poor, allowing different interpretations. You/we can only guess what the intended equation is supposed to be.

One tutor interpreted it like this:



That says the product of two expressions is zero. is not zero, so must be zero; that makes 5x = 1 and x = 1/5.

The probable intended interpretation is as shown by the other tutors:



That leads to , which leads to x = 5^1 = 5.

Yet another possible (and less likely) interpretation is this:



That leads to . With no base defined, that leads to , which leads to 5x = 10^1 = 10 and x = 2.
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