Express $$t=(\frac{1}{4})(log_a(\frac{10}{3}))$$ in exponential form $$a^y=x$$

Question

anonymous · Answer

Just do opposite of that:

anonymous · Answer

I'm really not seeing it, lol... we just learned log's today... and we didn't do one like this in class but regardless they confuse me... sigh.... Let me show you what I did...

anonymous · Answer

$$4t = Log_a(\frac{10}{3})$$

$$4t = Log_a(10) - Log_a(3)$$

$$4t.Log_a(a) + Log_a(3) = Log_a(10)$$

$$Log_a(3) + Log_a(a^{4t}) = Log_a(10)$$

$$Log_a(3a^{4t}) = Log_a(10)$$

Taking Antilogarithm, can you do it further???

anonymous · Answer

Why you deleted that @dpaInc ??
You have done it with very easy method...

anonymous · Answer

because you're explaining it with better fonts...:)

anonymous · Answer

@dpalnc, And you gave the second method to solve it..

anonymous · Answer

Sigh, it... crashed... but I think I see what to do...

anonymous · Answer

Is there any problem???

anonymous · Answer

I'll let you know... I don't think so... :)

anonymous · Answer

$$4t=log_a(10)-log_a(3)$$
$$log_a(a^{4t})+log_a(3)=log_a(10)$$
$$log_a(3a^{4t})=log_a(10)$$
$$a^{log_a(3a^{4t})}=a^{log_a(10)}$$
$$3a^{4t}=10$$
Yay... I hope I did that right...

anonymous · Answer

I didn't look at your answer above...

anonymous · Answer

But thanks so much everyone, I understand!!!

anonymous · Answer

That is very much true @purplec16..

anonymous · Answer

Welcome dear...