log[16] 32 = x + 3. explain the procedure used to solve this equation.

Question

anonymous · Answer

$$\log_{16} 32 = x + 3 \implies  \frac 5 4= x+3\implies x=12 $$

anonymous · Answer

$$\log_{16}32=x+3 $$
$$32=16^{x+3}$$
$$32=16^{x}*16^3$$
$$32/(16^3)=16^{x}$$
$$1/128=16^x$$
$$\log_{16}(1/128) = x $$
$$x = (\log_{10} (1/128))/(\log_{10} (16))$$
$$x=-1.75$$

radar · Answer

This is more realistic (I think), at least the procedure is outlined step by step.

anonymous · Answer

It checks on substitution as well...12 is not correct.

radar · Answer

I didn't think so, and the 5/4=x+3 with x=12 was confusing.

radar · Answer

5/4=x+3 comes out same as your answer -1.75

anonymous · Answer

Too many steps though, quicker still:
$$\log_{16} 32=x+3$$
$$\ln {32}/\ln{16}=x+3$$
$$x = (\ln32/\ln16) - 3$$
$$x = -1.75$$

anonymous · Answer

@FoolForMath please review your answer as it is marked best and @mape305 may believe it to be correct

radar · Answer

Just an algebraic "mis-step" he had the correct exponent for 16 to equal 32 (5/4).

anonymous · Answer

Indeed, just a typo in the end,$$\frac 5 4= x+3\implies 4x=-7 \implies x= -\frac 74$$