Finding the base in an exponential equation

Question

I'm trying to solve for $b$ in what seems like a very simple exponential equation: $b^{4.89}=1 182 795 699$

I know that $y=\log_b x$ is equivalent to $b^y=x$ but I don't know how that helps me to isolate $b$. I looked for the solution in WolframAlpha and it gives me $b=71.68$, but it won't show a step-by-step solution.

I would appreciate a lot if you could tell me how to solve this equation. Thanks :)

Answer 1

$$b^{4.89}=1 182 795 699$$ Taking natural $\log$ on both sides, $$\log b^{4.89}=\log1 182 795 699$$ $$4.89\log b=\log1 182 795 699$$ $$\log b=\frac{\log(1 182 795 699)}{4.89}$$ $$b=e^{\frac{\log(1 182 795 699)}{4.89}}$$

Answer 2

When you learn logs don't forget everything you know about roots!

$b^{4.89}=1 182 795 699$

So $(b^{4.89})^{\frac 1{4.89}} = 1,182,795,699^{\frac 1{4.89}}$

So $b = 1,182,795,699^{\frac 1{4.89}}=71.680456772641838989153714527019$

Answer 3

$$b^{4.89}=1 182 795 699$$ It is also equal to $$b^{489/100}=1182795699$$ Hence, $$b=1182795699^{100/489}$$