solve Log5(x-4)= Log7 X for X. Round your answer to four decimal places
and
for log y= log(0.5x-3)+ Log 2 state the domain,and express y as a function of x
anyone know?
Hi dan123,
Welcome to MHF! Please post only one question per thread in the future.
I am assuming by "log" you mean $\displaystyle \log_{10}$. In higher math, this can mean $\displaystyle \log_{e}=\ln$ so be careful and specific.
I'll help with your second question. Notice that log(x) has a real domain for x>0, not including 0. So use that to make some deductions. Firstly, 0.5x-3 > 0 for this to work but also log(0.5x-3) > 0 so that log(y) is defined. For what values of "a" is log(a) negative?
Really? Are you sure you have the problem solved? You can post your solution, including your steps here to be sure. It's not that simple of a question.
I would use this nice change of base formula:
$\displaystyle \log_{a}(b)=\frac{\ln(b)}{\ln(a)}$.
Change both sides using this method then combine terms using log rules.
Using the change of base rule:
Simple example: $\displaystyle log_2(5) = \frac{log_{10}(5)}{log_{10}(2)}$
More complicated example: $\displaystyle log_9(36) = \frac{ln(36)}{ln(9)} = \frac{ln(4)ln(9)}{ln(9)} = ln(4) = ln(2^2) = 2ln(2)$
You may choose to change to any base which is greater than 1 but most commonly you'd switch to either base 10 (first example) or base e (second example) as all calculators should have both these on
The change of base rule will allow you to pick a base supported by your calculator - usually base 10 or base e.
log base 7 X = $\displaystyle log_7(X)$
As is your calculator probably doesn't have a base 7 logarithm button (if it does feel free to evaluate it directly unless you're told to use the change of base)
The problem above can be converted to base 10, which should be on your calculator so you can punch in the numbers and solve:
$\displaystyle log_7(X) = \frac{log_{10}(X)}{log_{10}(7)}$