Can someone explain how this equation is solved along with the answer?

25^3x+2=125

Question

Can someone explain how this equation is solved along with the answer?

25^3x+2=125

anonymous · Answer

Can you double check your equation?

anonymous · Answer

Is that really 25^3?

anonymous · Answer

Also, this Equation too. 

$$\log_{6} x+ \log_{6} (x-5)=2$$

anonymous · Answer

@zordoloom $$25^{3x+2}=125$$

anonymous · Answer

Lake log base 25 of both sides you will get 3x+2=3/2 then isolate x you get 3x=-.5 x=-1/6

hartnn · Answer

can  u write 25 and 125 in powers of 5 ?

campbell_st · Answer

rewrite the equation in terms of powers of 5

$$(5^2)^{3x + 2} = 5^3$$

which becomes 

$$5^{6x + 4} = 5^3$$

just equate the powers now you have the same base and solve for x.

anonymous · Answer

Take not lake. Sorry

campbell_st · Answer

for the log question just rewrite it using log laws

$$\log(a) + \log(b) = \log (ab)$$

so you will have 

$$\log_{6}(x (x - 5)) = 2$$

next raise each term as a power of 6

$$a^{\log_{a}(b)} = b$$

so 

$$6^{\log_{6}(x(x-5)} = 6^2$$

or

$$x(x -5) = 36$$

solve for x