Logarithms, please help?!?

Question

solve the equation by changing the base of the logarithm to 10. thank you!

log(sub 2)x+log(sub 4)x=log(sub 2)5

Answer 1

Formula for changing base of logarithm:

log(base b)x = log(base a)x/log(base a)b

So, logx designates decimal logarithm of x:

log(base 2)x = logx / log2

log(base 4)x = logx / log4 = logx / 2log2

The equation becomes:

logx/log2 + logx/2log2 = log5/log2

logx + (1/2)logx = log5

(3/2)logx = log5

logx = (2/3)log5 = log(5^2/3)

x = 5^2/3

x = cubic root of 25

Answer 2

logx/log2+logx/log4=log5/log2

logx+1/2*logx/log2=log5/log2

3logx=log5

logx^3=log 5

x^3=5