Logarithm Question...

[Samara]

Hello. I am currently studying for am algebra test. I am attempting a problem that I do not understand, but would like to understand it before the test. I am not looking for the answer, but rather, some assistance please. Any help at all would be greatly appreciated!

 

[lookagain]

Edit: Another handy thing to know about logs is this: \(\displaystyle log_b(m) = n \implies b^n = m, and\ b^n = m \implies log_b(m) = n.\)

So \(\displaystyle \log_b(b) = 1, and\ log_b(1) = 0\ for\ any\ real\ positive\ b\) and b cannot equal 1.

DefinitionThe logarithm of a number x with respect to base b is the exponent to which b has
to be raised to yield x. In other words, the logarithm of x to base b is the solution y
of the equation^[2]

The logarithm is denoted "log_b(x)" (pronounced as "the logarithm of x to base b" or
"the base-b logarithm of x"). In the equation y = log_b(x), the value y is the answer
to the question "To what power must b be raised, in order to yield x?". For the
logarithm to be defined, the base b must be a positive real number not equal to
1 and x must be a positive number.^{[nb 2]}

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