f(x)= log10^x and g(x) = 3x-1 what is f(x) *g(x)

Question

anonymous · Answer

@hartnn Can you help me please :)

campbell_st · Answer

well the way the question is written and using some log laws

$$\log 10^x = x$$

so 

f(x) = x

then f(x)*g(x) = x(3x -1)

anonymous · Answer

Ok! you broke it up

campbell_st · Answer

well given the way the question is written is assumed it was a base 10 log... 

so I simplified f(x)...

anonymous · Answer

Oh cause the only thing like that is (3x-1)^x

anonymous · Answer

or log10x^3x-1

campbell_st · Answer

ok... I understand the question now 

its 

$$f(x) = \log_{10} (x)$$

g(x) = 3x -1

find 

$$f(x) \times g(x)$$

which is 

$$(3x -1) \times \log_{10}(x)$$

applying the log law form multiplication you get 

$$\log_{10}x^{3x -1}$$

that's an answer choice...

anonymous · Answer

Ok im omw to the library...so ill be back in 4 minutes haha thank you so far

anonymous · Answer

@campbell_st im back

anonymous · Answer

can you help with 2 more?

anonymous · Answer

if f(x)= log3(x+1) what is f^-1(2)

campbell_st · Answer

ok... so to find the inverse write you equation as 

$$x = \log_{3}(y + 1)$$

to find the inverse... make y the subject of the equation above...

anonymous · Answer

ok so rewrite it?

campbell_st · Answer

well I've done that

whats the opposite of taking a log...?

anonymous · Answer

anti log

campbell_st · Answer

well its raising it to the power of the base... 

$$\log_{a}(b) = x .... then ...a^{\log_{a}(b)} = a^x$$

which becomes 

$$b = a^x$$

so this is the log law you need for this problem 

$$3^{\log_{3}(y + 1)} = 3^x$$

so after simplifying you get

$$y + 1 = 3^x$$

so what's the final equation with y as the subject.

anonymous · Answer

y=1?

anonymous · Answer

wait

anonymous · Answer

y= 3^x -1/

campbell_st · Answer

nearly you forgot a piece 

$$y = 3^x - 1$$

campbell_st · Answer

so this is the inverse equation 

$$f^{-1}(x) = 3^x - 1$$

campbell_st · Answer

just substitute x = 2 and evaluate for the inverse...

anonymous · Answer

idk how

campbell_st · Answer

well just evaluate 

$$f^{-1}(2) = 3^2 - 1$$

anonymous · Answer

hm ok how do I get the 2 out of paren

campbell_st · Answer

you don't what if left hand side is saying is ... whats the value of the equation when x = 2

so you need to find the value of 

$$3^2 - 1=$$

anonymous · Answer

9-1 = 8 !