SOLVE EQUATION FOR X: log_16 8=x?

log_16(8) = x

16^(log_16(8)) = 16^x

8 = 16^x

log(8) = log(16^x)

log(2^3) = x * log(2^4)

3*log(2) = 4x*(log(2))

x = (3*log(2))/(4*log(2))

x = (3/4) * log(2)/log(2)

x = 3/4 * 1

x = 3/4

log_16 8 = Ln 8/Ln 16 = 3/4

or

log_16 8 = log_16 sqrt(64)

=(1/2)log_16 64

=(1/2)log_16 4^3

=(3/2)log_16 4

=(3/2)log_16 sqrt(16)

=(3/4)log_16 16

=3/4

log_16 8=x

It says 16^x = 8

(2^4)^x = 2^3

2^(4x) = 2^3

so , 4x = 3

x=3/4

I hope it clears ...

log[16] 8 = x

Hint: [16] is a base.

=> 16 & 8 in index forms are 2⁴ & 2³ respectively, then

log[2⁴] 2³ = x

=> In logarithms, log[2²] a = 1/2 log[2] a, then by applying this rule, you'll have

1/4 log[2] 2³ = x

=> In logarithms, log a^b = blog a, then by applying this rule, you'll have

3/4 log[2] 2 = x

=> In logarithms also, log[a] a = 1, then

3/4 * 1 = x

3/4 = x

Hence x = 3/4 ...Ans.

log_16 8=x

log8/log16=x

3log2/(4log2)=x

x=3/4

x = log_16(8)

x = log_2(8) / log_2(16)

x = log_2(2^3) / log_2(2^4)

x = 3 / 4

8=16^X

2^3=2^4X

3=4X

X=3/4