de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

162^{sqrt(x+3)}>4^{x-2}

Lösung

16 2^{x + 3} > 4^{x - 2}

Lösung

- 3 \leq x < \frac{16 ln ^{2} ( 2 ) + ln ^{2} ( 162 ) + ln ^{4} ( 162 ) + 80 ln ^{2} ( 2 ) ln ^{2} ( 162 )}{8 ln ^{2} ( 2 )}

+2

Intervall-Notation

- 3, \frac{16 ln ^{2} ( 2 ) + ln ^{2} ( 162 ) + ln ^{4} ( 162 ) + 80 ln ^{2} ( 2 ) ln ^{2} ( 162 )}{8 ln ^{2} ( 2 )}

Dezimale

- 3 \leq x < 19.34976 \dots

Schritte zur Lösung

16 2^{x + 3} > 4^{x - 2}

Wenn

f (x) > g (x)

dann

ln (f (x)) > ln (g (x))

ln (16 2^{x + 3}) > ln (4^{x - 2})

Vereinfache

ln (16 2^{x + 3}) : ln (162) x + 3

Vereinfache

ln (4^{x - 2}) : 2 ln (2) (x - 2)

ln (162) x + 3 > 2 ln (2) (x - 2)

ln (162) x + 3 > 2 ln (2) (x - 2) : - 3 \leq x < \frac{16 ln ^{2} ( 2 ) + ln ^{2} ( 162 ) + ln ^{4} ( 162 ) + 80 ln ^{2} ( 2 ) ln ^{2} ( 162 )}{8 ln ^{2} ( 2 )}

- 3 \leq x < \frac{16 ln ^{2} ( 2 ) + ln ^{2} ( 162 ) + ln ^{4} ( 162 ) + 80 ln ^{2} ( 2 ) ln ^{2} ( 162 )}{8 ln ^{2} ( 2 )}

Graph

Beliebte Beispiele

2^{x} < 16

8^{x - 2} > 16

2^{y} + 4 > 32

3^{2x+3}+3^{x+1}-4>0

3^{2 x + 3} + 3^{x + 1} - 4 > 0

2^{n} - 1 > 1000000