Step-by-step explanation:
I'll help with the first couple so you can understand how to do the rest!
1) Now the instructions say to rewrite with the same base, that means that the number under the exponent has to be the same on both sides of the equal sign. The common factor between 125 and 25 is 5.
5²=25 and 5³=125 therefore 5 is your same base
Using this base rewrite each side;
5³⁽²ˣ⁾=5² ---> 5⁶ˣ=5²
Because the bases are the same now the exponents have to be the same which means you can set them equal and solve;
6x=2 ---> x=2/6 ---> x=1/3
2) So here you can't reduce 2 so you need to find the power that makes 2 equal 64 (it's 6). Once you have the exponent you can rewrite it to make the bases the same;
2³ˣ⁻³=2⁶
Since the bases are the same, we can set the exonents equal and solve!
4) The key for these is to remember this; logₐ(x)=n is also aⁿ=x and vise versa!
So here we have;
6⁴ˣ=234 --> log6(234)=4x --> log6(234)/4=x --> x=0.7612
I hope this helps! I'll reply to any comments or questions you have!
