A logarithmic exponential equation with different bases

[Nikolas111]

Could somebody help me with this equation please ? :? I got stuck after my third step when I got these logarithms on the same bases 1.( log₂ x³ /log₂4) +log₂ √x=8
2. (log₂ x³ /2) +log₂√x=8 // because log₂4 =2
3. log₂ x³ +2log₂√x=16
After this step I didn't know how to continue.
Thank you in advance.

 

[Deleted member 4993]

Could somebody help me with this equation please ? :? I got stuck after my third step when I got these logarithms on the same bases 1.( log₂x³ /log₂4) +log₂ √x=8
2. (log₂x³ /2) +log₂√x=8 // because log₂4 =2

3. 1/2*(log₂x³) +1/2*(log₂ x) = 8

4.(log₂x⁴) = 16

5. x⁴ = 2¹⁶

Continue....
3. log₂x³ +2log₂√x=16
After this step I didn't know how to continue.
Thank you in advance.

.

 

[pka]

Could somebody help me with this equation please ?

First note that \(\displaystyle \log_b(a)=\dfrac{\log(a)}{\log(b)}\) thus what you have is
\(\displaystyle \dfrac{3\log(x)}{2\log(2)}+\dfrac{\log(x)}{2\log(2)}=2^3\)

 

[Nikolas111]

logarithmic exponential equation with different bases

I tried to continue x=log _{2^16 / log 4} but the answer which came out was x=8 which is wrong because the correct answer is 16 . Where did I make a mistake ? :-?

Thank you for helping me.