Block 5: Exponentials
Problem 1: Solve in R:
a) 3x
+ 3x+1
− 5x−1
= 5x
− 3x+3
+ 5x+2
b) 4
25
x+3
· 125
8
4x−1
= 5
2
c) 4x
− 2x+1
− 8 = 0
d) 51−x
= 7x−1
e) 2x+1
+ 3 · 22+x
≤ 2x+5
Problem 2: Sketch a graph of a function:
a) y = 2x
b) y = 3−x
c) y = 1
3
x
d) y = log2 x
e) y = log0.5 x
Block 6: Logarithms
Problem 1: Find:
a) (
√
2)log2
1
4
+2 log10 100
+ 1
3
log3 27 − log3 1
b) x, if log1
3
x = −2
5
,
c) x, if logx
27
2
= −2,
Problem 3: Solve:
a) log10 x + 3
log10 x
= 4,
b) log10
√
x + 1 + log10
√
x − 1 = 2 − log10 2,
c) 5 log10 x+3
3 log10 x−4
= log10 x+5
3 log10 x−4
− 2,
d) log0.5 (log0.2(x) + 2) < 3
e) log3 (3 + log2(x)) < 3
f) log3 (log0.5 (log10(x))) > 1