Question

consider the equation 10 2z/3=15.
solve the equation for z.
express the solution as a logarithm base-10
z=
approximate the value of z. round your answer to the nearest thousandth
z=

Answer 1

Hi there! :)

$\large\boxed{z = 1.764}$

$10x^{(2z/3)} = 15$

Rewrite as a logarithmic equation using this format:

$a^{b} = c \\\\log_{a}c = b$

In this instance:

a = 10 (log is by default base 10)

b = 2z / 3

c = 15

Rewrite as the log equation:

$log 15 = 2z/3$

Evaluate log (15):

$1.176 = 2z / 3$

Multiply both sides by 3:

$3.528 = 2z$

Divide both sides by 2:

$z = 1.764$