3 years ago

Solve the following exponential equations. 10^(3x−5) = 7^x

Mathematics

1 answer:

zalisa [80]3 years ago

4 0

Answer:

x = 2.3202

Step-by-step explanation:

Given equation:

$10^{(3x-5)} = 7^x$

on taking log both sides, we get

$\log(10^{(3x-5))} =\log(7^x)$

now,

using the property of log function

log(aᵇ) = b × log(a)

therefore,

we get

(3x-5)log(10) = xlog(7)

now,

log(10) = 1

and

log(7) = 0.84509

thus,

( 3x - 5 ) × 1 = 0.84509x

3x - 0.84509x - 5 = 0

2.15491x = 5

x = 2.3202

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