Professor Cardy

web
statistics

Em $$f: \mathbb{R}_+^{**} -> \mathbb{R}$$, onde $$f(x)= log_b x$$ o gráfico de $$f$$ no Plano Cartesiano:

Se $$b > 1$$ $$f$$ é crescente

Se $$0 < b <1$$ $$f$$ é decrescente

Para $$b >1$$ $$f: \mathbb{R}_+^{**} -> \mathbb{R}$$, onde $$f(x)= log_b x$$ terá gráficos como esses:

$$f_1 (x) = log_2 x$$ base $$2$$. Passa pelos pontos $$(1,0)$$, $$(2,1)$$, ... $$(t, log_2 t)$$.

$$f_2 (x) = log_3 x$$ base $$3$$. Passa pelos pontos $$(1,0)$$, $$(3,1)$$, ... $$(t, log_3 t)$$.

$$f_3 (x) = log_4 x$$ base $$4$$. Passa pelos pontos $$(1,0)$$, $$(4,1)$$, ... $$(t, log_4 t)$$.

$$f_4 (x) = log_5 x$$ base $$5$$. Passa pelos pontos $$(1,0)$$, $$(5,1)$$, ... $$(t, log_5 t)$$.

$$f_5 (x) = log_6 x$$ base $$6$$. Passa pelos pontos $$(1,0)$$, $$(6,1)$$, ... $$(t, log_6 t)$$.

Para $$0 < b < 1$$ $$f: \mathbb{R}_+^{**} -> \mathbb{R}$$, onde $$f(x)= log_b x$$ terá gráficos como esses:

$$f_1 (x) = log_{1/2} x$$ base $$1/2$$. Passa pelos pontos $$(1,0)$$, $$(1/2, 1)$$, ... $$(t, log_{1/2} t)$$.

$$f_2 (x) = log_{1/3} x$$ base $$1/3$$. Passa pelos pontos $$(1,0)$$, $$(1/3, 1)$$, ... $$(t, log_{1/3} t)$$.

$$f_3 (x) = log_{1/4} x$$ base $$1/4$$. Passa pelos pontos $$(1,0)$$, $$(1/4, 1)$$, ... $$(t, log_{1/4} t)$$.

$$f_4 (x) = log_{1/5} x$$ base $$1/5$$. Passa pelos pontos $$(1,0)$$, $$(1/5, 1)$$, ... $$(t, log_{1/5} t)$$.

$$f_5 (x) = log_{1/6} x$$ base $$1/6$$. Passa pelos pontos $$(1,0)$$, $$(1/6, 1)$$, ... $$(t, log_{1/6} t)$$.