Logarithmic and Exponential Functions(Senior Class Math Study by Topics Test ) : Gate Academy

Welcome to your Logarithmic and Exponential Functions(Senior Class Maths Study by Topics)

NAME

PHONE NUMBER

Evaluate:

log₃324 - 2 log₃6

Simplify :
2^-3x 16^3/4x 2⁰

1/2

Solve for x
2^2x - 6(2^x) = - 8

-1

Solve the equation (1/2)^{2x + 1} = 1

-1/2

-2

1/2

Evaluate , without calculator, the logarithmic expression:
log₃ 27

Solve for x in the logarithmic equation:
log_5.6 x = 0

-1

Evaluate:

-3/2

1/5

-2/3

Solve for x the equation 4^{x - 2} = 3^{x + 4}

ln(4/3)

4 ln(6)

4 ln(6) / ln(4/3)

4 ln(6) / ln(4)

Change the given exponential expressions into logarithmic expressions:
x² = a

a = log a

2 = log x (a)

a = log x (2)

2 = log x

10.

Evaluate , without calculator, the logarithmic expression:
log_b 1 with b > 0 and b ≠ 0

-1

11.

Given that y³=log₁₀100000000, find y

12.

Evaluate:

(3⁰- 9^-1/2)^-3

2/3

3/2

27/8

1/9

13.

Solve for x
4 ^{2x + 1} = 16

1/3

1/5

1/2

1/4

14.

If log₁₀2 = 0.3010,
the number whose logarithm is

equals

0.006

0.06

0.008

0.08

15.

Evaluate:
log 0.225
if log 3 = 0.477 and log 5 = 0.699

-0.352

-1.352

-0.648

-1.648

16.

Evaluate:

17.

Solve x y^m = yx³ for m

2 + In(x)

ln(x) / ln(y)

1 + 2 ln(x) / ln(y)

In(x/y)

18.

Solve for a:

2log₈a – 5log₈a = 2

1/2

1/4

19.

Simplify:

20.

Solve for x the equation ln (x - 1) + ln (2x - 1) = 2 ln (x + 1)

-5

-4

21.

Find the value of x if

log₄x = 3.5

256

128

22.

Find the value of x if

1/2 log₁₀x = 1

100

√10

1/√10

0.01

23.

Solve the equation:
3x-² = 4/27

9/2

2/9

4/81

81/4

24.

Solve for x
(1 / 2) ^x = 2

-1

25.

Change the given exponential expressions into logarithmic expressions:
3^x = m

x = log 3 (m)

3 = log x (m)

m = log 3 (x)

m = log 3

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