How do you solve the equation ${log}_{10} z + {log}_{10} (z + 3) = 1$ $log_10z+log_10(z+3)=1$ ?

Question

How do you solve the equation ${log}_{10} z + {log}_{10} (z + 3) = 1$ $log_10z+log_10(z+3)=1$ ?

1 Answer

Impact of this question

2606 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-11T15:00:11

${2}$ ${2}$

Explanation:

Use the rule ${log}_{a} n + {log}_{a} m = {log}_{a} (n \cdot m)$ $log_a n + log_a m = log_a(n * m)$ .

${log}_{10} z + {log}_{10} (z + 3) = 1$ $log_10 z + log_10(z + 3) = 1$

${log}_{10} (z (z + 3)) = 1$ $log_10(z(z + 3)) = 1$

Convert to exponential form.

$z^{2} + 3 z = 10^{1}$ $z^2 + 3z = 10^1$

$z^{2} + 3 z = 10$ $z^2 + 3z = 10$

$z^{2} + 3 z - 10 = 0$ $z^2 + 3z - 10 = 0$

$(z + 5) (z - 2) = 0$ $(z + 5)(z - 2) = 0$

$z = - 5 and 2$ $z = -5 and 2$

However, $z = - 5$ $z = -5$ is extraneous.

Hopefully this helps!

Science

Math

Humanities

... and beyond

How do you solve the equation ${log}_{10} z + {log}_{10} (z + 3) = 1$ $log_10z+log_10(z+3)=1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the equation log10z+log10(z+3)=1log_10z+log_10(z+3)=1?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve the equation ${log}_{10} z + {log}_{10} (z + 3) = 1$ $log_10z+log_10(z+3)=1$ ?