Question

how would I solve this??
logx^125 = -3​

Answer 1

Step-by-step explanation:

First, this is how I read it.

$\log(x^{125})=-3$

Next, this is how logarithms work:

$b^y=x\implies \log_b(x)=y$

In your equation, we have all 3 numbers:

• b = 10 (implied)

• x = $x^{125}$

• y = -3

With that information, you can convert the logarithm into "normal" form:

$10^{-3}=x^{123}$

The negative power rule $x^{-a}=\frac{1}{x^a}$ is also useful here.

Now, just solve for x:

$x^{125}=\frac{1}{10^3}\\x^{125}=\frac{1}{1000}\\x=\sqrt[125]{\frac{1}{1000}}\\x=\frac{1}{\sqrt[125]{1000} }$

That's about as simplified as it gets, unless you want this:

$x=\frac{1}{10^{\frac{3}{125}}}$

Thats 10^(3/125), numbers got very small.

I'm still not confident I understood the problem correctly, so let me know if I need to fix anything.