How do you solve $log_3z=4log_z3$ ?

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Answer 1 · 2016-01-29T16:10:47

$z=9$

Rewrite everything using the change of base formula.

The change of base formula provides a way of rewriting a logarithm in terms of another base, like follows:

$log_ab=log_cb/log_ca$

In this case, the new base I will choose is $e$ , so we will use the natural logarithm.

$log_3z=4log_z3$

$=>lnz/ln3=(4ln3)/lnz$

Cross multiply.

$=>(lnz)^2=4(ln3)^2$

Take the square root of both sides.

$=>lnz=2ln3$

We can modify the right hand side using the rule: $b*lna=ln(a^b)$

$=>lnz=ln(3^2)=ln9$

Use the fairly intuitive rule that if $lna=lnb$ , then $a=b$ .

$=>z=9$

How do you solve log_3z=4log_z3log_3z=4log_z3?