Find value of
log (base 8)log (base 2) log (base 3)log (base 3) (27)^3
I endedup with 1.000063462 which was wrong
zero.
If you want to use a calculator to evaluate the above expression, you will need to understand the above expression is evaluated from right to left, so appropriate sets of parentheses must be inserted.
In fact, the above expression can be evaluated mentally to a simple fraction.
log (base 8)log (base 2) log (base 3)log (base 3) (27)^3
should be written as follows (square brackets have been inserted):
log (base 8) [log (base 2) [ log (base 3) [ log (base 3) (27)^3 ] ] ]
Start evaluating from the innermost set of brackets outwards.
To find the value of log (base 8) log (base 2) log (base 3) log (base 3) (27)^3, let's break it down step by step:
Step 1: Start by simplifying the expression by applying the logarithmic property log (base c) c = 1.
log (base 8) log (base 2) log (base 3) log (base 3) (27)^3
Step 2: Simplify the expression log (base 3) log (base 3) (27)^3 by applying the exponential property log (base c) c^x = x.
log (base 8) log (base 2) log (base 3) 3^3
Step 3: Simplify the expression log (base 3) 3^3 by applying the exponential property log (base c) c^x = x.
log (base 8) log (base 2) log (base 3) 27
Step 4: Evaluate the expression log (base 3) 27 by using the logarithmic property log (base c) c^x = x.
log (base 8) log (base 2) 3
Step 5: Evaluate the expression log (base 2) 3 by using the logarithmic property log (base c) c^x = x.
log (base 8) log (base 2) 3
Step 6: Evaluate the expression log (base 8) 3 by using the logarithmic property log (base c) c^x = x.
log (base 8) log (base 2) 3
At this point, we cannot simplify the expression any further, as we don't know the values for log (base 8) and log (base 2). Therefore, we cannot determine the exact numerical value of the expression without further information.
To find the value of the given expression, let's break it down step by step:
Step 1: Consider the innermost logarithm:
log (base 3) (27)^3
The exponent of 3 in the base matches the power of 3, so this simplifies to:
log (base 3) (3^3)
log (base 3) (27)
Since the base matches the argument, the logarithm evaluates to 1. Therefore:
log (base 3) (27)^3 = 1^3
Step 2: Now we move to the outer logarithm:
log (base 8) log (base 2) log (base 3) 1^3
log (base 8) log (base 2) 1
Since the argument of the logarithm is 1, the logarithm evaluates to 0. Therefore:
log (base 8) log (base 2) log (base 3) (27)^3 = log (base 8) log (base 2) 0
Step 3: Finally, let's evaluate the outermost logarithm:
log (base 8) log (base 2) 0
The logarithm of 0 is undefined since there is no value for x when 2^x equals 0. Therefore, the value of the expression is undefined.
Hence, the value you obtained (1.000063462) is incorrect. The correct value is undefined.