Use change of base to rewrite the expression, log5 16
When I solved this, I got log10 16 / log10 5
But when checking it on mathway I got log 16 / log 5
Could someone explain this?
it's a semantics thing ... if no base is indicated , 10 is assumed
the base does not matter. logb16/logb5 = log516
To rewrite the expression log5 16 using change of base, we can use the formula:
logb a = logc a / logc b
where logb a represents the logarithm of a with base b.
For the given expression log5 16:
We can rewrite it as log10 16 / log10 5 using the formula. This means we are finding the logarithm of 16 with base 10, divided by the logarithm of 5 with base 10.
When you checked it on mathway and got log 16 / log 5, it seems that mathway used the common logarithm (base 10) as the default base, so there was no need to explicitly mention it.
In summary, both log10 16 / log10 5 and log 16 / log 5 represent the same concept and yield the same result. The difference lies in explicitly specifying the base or using the default base when expressing the logarithms.
Certainly! The expression log5 16 can be rewritten using the change of base formula. This formula allows you to change the base of a logarithm to a different base.
The change of base formula is: logb y = logx y / logx b
In this case, we want to rewrite log5 16 using a different base, let's say base 10.
Applying the change of base formula, we have:
log5 16 = log10 16 / log10 5
Your initial answer of log10 16 / log10 5 is correct. This is because the logarithm function typically defaults to base 10 when no base is indicated. So, mathematically, log 16 is referring to log10 16.
However, the answer you obtained using Mathway, log 16 / log 5, is also correct. This is because some calculators or software programs, like Mathway, interpret log without a base as log10.
So, both log10 16 / log10 5 and log 16 / log 5 are equivalent and correct representations of log5 16. The difference lies in the interpretation of the logarithm function in different contexts.