Question

Find x : log 4(2x+3)=3/2​

Answer 1

$log \: 4(2x + 3) = \frac{3}{2} \\ \\ 2 \: log (8x + 12) = 3 \\ \\ log {(8x + 12)}^{2} = log(1000) \\ \\ {(8x + 12) }^{2} = 1000 \\ \\ 8x + 12 = 10 \sqrt{10} \\ \\ 8x = 10 \sqrt{10 } + 12 \\ \\ x = \frac{10 \sqrt{10} + 12}{8} = \frac{5 \sqrt{10} + 6 }{4}$

Hence your answer.

Answer 2

answer:

log4(2x+4)=3/2

4^3/2=2x+3

2^2×3/2=2x+3

2^3=2x+3

8=2x+3

2x=3+8

2x=5

x=5/2