fertilizeki

2021-12-31

How to find the value of an unknown exponent?

E.g. I have the question:

${2}^{4x+1}=128$

I solved this by knowing that$128={2}^{7}$ and therefore x must equal $1.5$ .

However, is there a way of solving this without knowing that$128={2}^{7}$ ?

E.g. I have the question:

I solved this by knowing that

However, is there a way of solving this without knowing that

yotaniwc

Beginner2022-01-01Added 34 answers

... and without logarithms or knowing any powers of 2 other than the most trivial one ...

${2}^{4x+1}=128$

${2}^{4x+1-1}={2}^{4x}=\frac{128}{2}=64$

${2}^{4x-1}=32$

${2}^{4x-2}=16$

${2}^{4x-3}=8$

${2}^{4x-4}=4$

${2}^{4x-5}=2$

$2}^{4x-6}=1={2}^{0$

so$4x-6=0$ and $x=\frac{6}{4}=\frac{3}{2}$ .

so

Nadine Salcido

Beginner2022-01-02Added 34 answers

Vasquez

Expert2022-01-09Added 669 answers

note that you can use any logarithm, log base 10 or '

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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