Question

the logorithmic form of 64 =2^6 is __________. and the exponential form of log1024 to base 4 =5 is__________

Answer 1

Heya user ,
Here is your answer !!

The logarithmic form of 64 = 2^6 is __ log 64 to the base 2 is 6 __ .

The exponential form of log1024 to base 4 =5 is__ 4^5 = 1024 __ .

Hope it helps !!

Answer 2

Answer:

The logarithm form of

$64 = {2}^{6} is \: log_{2}(64) = 6$

The exponential form of

$log_{4}(1024) = 5 \: is \: 1024 = {4}^{5}$

Step-by-step explanation:

• Logarithm is the exponent to which base must be raised to give a certain number. In other words, logarithm is the inverse of exponents.
• Logarithm is defined as

$log_{b}(x) = y$

• where, b = base; y = exponent and x = power.
• In exponential form this can be written as:

$x= {b}^{y}$

• Given that:

$64 = {2}^{6} \\ taking \: logarithm \: om \: both \: sides \\ log(64) = log( {2}^{6} ) \\ log(64) = 6 \: log(2) \\ \frac{ log(64) }{ log(2) } = 6 \\ log_{2}(64) = 6$

• Given that:

$log_{4}(1024) = 5 \\ \frac{ log(1024) }{ log(4) } = 5 \\ log(1024) = 5 \: log(4) \\ log(1024) = log( {4}^{5} ) \\taking \: antilog \: on \: both \: sides \\ 1024 = {4}^{5}$