can someone show me the steps to solve this equation?

Given the function f(x)=0.3(4)^x, what is the value of f^-1(6) @campbell_st

Question

can someone show me the steps to solve this equation?

Given the function f(x)=0.3(4)^x, what is the value of f^-1(6) @campbell_st

campbell_st · Answer

well you need to find the inverse of the function 1st

so swap x and y and you have 

$$x = 0.3 \times 4^y$$

now make y the subject of the equation...

anonymous · Answer

ok so would you square the equation?

anonymous · Answer

@campbell_st

campbell_st · Answer

nope you wouldn't square the equation... 

the 1st step is to divide both sides of the equation by 0.3

$$\frac{x}{0.3} = 4^y$$

whats the opposite of an exponent..?

anonymous · Answer

squaring the equation

campbell_st · Answer

nope.. sorry... that's not the opposite of an exponential

anonymous · Answer

hmmm would you multiply the 4 across the equation?

campbell_st · Answer

nope.... thats not it.... you need to find the opposite of an exponential

anonymous · Answer

oooh sorry, it would be something to do with log right?

anonymous · Answer

@campbell_st

anonymous · Answer

so it would be log4(x/3)=y?

campbell_st · Answer

thats right 

so 

$$\log(\frac{x}{0.3}) = y \times \log(4)$$

so whats the next step

anonymous · Answer

ok hold on let me think about it

campbell_st · Answer

The only problem with taking a base 4 log is that you will need to use change of base at some point to evaluate the solution if your calculator only does base e or base 10 logs

anonymous · Answer

$$\log(x \div 3)/\log(4)=y$$

anonymous · Answer

is that looking correct @campbell_st

campbell_st · Answer

thats it... now substitute x = 6 and evaluate

campbell_st · Answer

except its 0.3.... not 3

anonymous · Answer

thank you :D @campbell_st

anonymous · Answer

ok the answer is 2.161 :DDDDD

anonymous · Answer

@campbell_st

campbell_st · Answer

thats what I got